Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2964 conjugacy classes of subgroups; only the 654 normal subgroups are shown.
This group has 2964 conjugacy classes of subgroups — too many to draw. Only its 654 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D9 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C22×C9×D8 | C2 |
| socle | C23×C3 | D3×D4 |
| hypercenter | C22×D8 | D9 |
| hypocenter | C9 | C23×D8 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×D9 | C2 | semidirect |
| 2. C22×C9×D8 | C2 | semidirect |
| 3. C22×#3673 | C2 | semidirect |
| 4. C2×D8×D9 | C2 | direct (N × H) |
| 5. C22×D72 | C2 | semidirect |
| 6. C22×C8×D9 | C2 | semidirect |
| 9. C22×D4×C9 | C22 | semidirect |
| 12. C2×D4×D9 | C22 | semidirect |
| 13. C22×D36 | C22 | semidirect |
| 15. C2×C9×D8 | C22 | semidirect |
| 16. C22×C8×C9 | C22 | semidirect |
| 17. C2×#3673 | C22 | semidirect |
| 18. C22×C9⋊C8 | C22 | semidirect |
| 19. D8×D9 | C22 | direct (N × H) |
| 20. C2×D72 | C22 | semidirect |
| 21. C2×C8×D9 | C22 | semidirect |
| 34. C2×D4×C9 | C23 | semidirect |
| 39. D4×D9 | C23 | semidirect |
| 41. C2×D36 | C23 | semidirect |
| 44. C9×D8 | C23 | semidirect |
| 45. C2×C8×C9 | C23 | semidirect |
| 46. #3673 | C23 | semidirect |
| 47. C2×C9⋊C8 | C23 | semidirect |
| 48. D72 | C23 | semidirect |
| 49. C8×D9 | C23 | semidirect |
| 72. C22×D9 | D8 | direct (N × H) |
| 75. D4×C9 | C24 | semidirect |
| 81. D36 | C24 | semidirect |
| 84. C8×C9 | C24 | semidirect |
| 85. C9⋊C8 | C24 | semidirect |
| 90. C22×D8 | D9 | direct (N × H) |
| 116. C22×C9 | C2×D8 | semidirect |
| 121. C2×D9 | C2×D8 | direct (N × H) |
| 131. C22×D4 | C2×D9 | semidirect |
| 136. C2×D8 | C2×D9 | direct (N × H) |
| 139. C22×C8 | C2×D9 | semidirect |
| 162. C2×C9 | C22×D8 | semidirect |
| 165. D9 | C22×D8 | direct (N × H) |
| 177. C2×D4 | C22×D9 | semidirect |
| 184. D8 | C22×D9 | direct (N × H) |
| 187. C2×C8 | C22×D9 | semidirect |
| 200. C9 | C23×D8 | semidirect |
| 214. D4 | C23×D9 | semidirect |
| 221. C8 | C23×D9 | semidirect |
| 234. C22 | D8×D9 | direct (N × H) |
| 243. C2 | C2×D8×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D9 | 2 |
| C22×C9×D8 | 2 |
| C22×#3673 | 2 |
| C2×D8×D9 | 2 |
| C22×D72 | 2 |
| C22×C8×D9 | 2 |
| C22×D3×D8 | 3 |