Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2964 conjugacy classes of subgroups; only the 814 normal subgroups are shown.
This group has 2964 conjugacy classes of subgroups — too many to draw. Only its 814 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | #611 |
| commutator, cosocle | C4×C9 | C25 |
| Frattini | C3×C4 | C24×D3 |
| Fitting | C23×D4×C9 | C2 |
| socle | C24×C3 | #67 |
| hypercenter | C23×D4 | D9 |
| hypocenter | C9 | C23×D8 |
| LCS | G ▷ C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D4×C9 | C2 | semidirect |
| 2. C23×D36 | C2 | semidirect |
| 3. C22×#3673 | C2 | direct (N × H) |
| 4. C23×C9⋊C8 | C2 | semidirect |
| 9. C22×D4×C9 | C22 | semidirect |
| 12. C22×D36 | C22 | semidirect |
| 13. C2×#3673 | C22 | direct (N × H) |
| 14. C22×C9⋊C8 | C22 | semidirect |
| 25. C2×D4×C9 | C23 | semidirect |
| 29. C2×D36 | C23 | semidirect |
| 30. #3673 | C23 | direct (N × H) |
| 31. C2×C9⋊C8 | C23 | semidirect |
| 44. C23×C9 | D8 | semidirect |
| 49. D4×C9 | C24 | semidirect |
| 53. D36 | C24 | semidirect |
| 54. C9⋊C8 | C24 | semidirect |
| 56. C23×D4 | D9 | semidirect |
| 74. C22×C9 | C2×D8 | semidirect |
| 85. C22×D4 | C2×D9 | semidirect |
| 103. C2×C9 | C22×D8 | semidirect |
| 114. C2×D4 | C22×D9 | semidirect |
| 127. C9 | C23×D8 | semidirect |
| 132. C23 | #3673 | direct (N × H) |
| 137. D4 | C23×D9 | semidirect |
| 149. C22 | C2×#3673 | direct (N × H) |
| 156. C2 | C22×#3673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C9 | 2 |
| C23×D36 | 2 |
| C22×#3673 | 2 |
| C23×C9⋊C8 | 2 |
| C23×#213 | 3 |