Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
569 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 569 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#467 | C2 | semidirect |
| 3. C2×C3×#828 | C2 | semidirect |
| 4. C3×#4549 | C2 | semidirect |
| 5. C3×#4491 | C2 | semidirect |
| 7. #71085 | C3 | direct (N × H) |
| 9. C2×C32×Q16 | C22 | semidirect |
| 15. C32×#107 | C22 | semidirect |
| 18. C2×C3×C3⋊C16 | C22 | semidirect |
| 23. C3×#467 | D3 | semidirect |
| 24. C3×#467 | C2×C3 | semidirect |
| 25. C2×#828 | C2×C3 | semidirect |
| 28. #4549 | C2×C3 | semidirect |
| 29. #4491 | C2×C3 | semidirect |
| 52. C2×C3×Q16 | C2×D3 | semidirect |
| 53. C2×C3×Q16 | C22×C3 | semidirect |
| 69. C3×#107 | C2×D3 | semidirect |
| 70. C3×#107 | C22×C3 | semidirect |
| 75. C2×C3⋊C16 | C22×C3 | semidirect |
| 96. #467 | C3×D3 | semidirect |
| 146. C22×C32 | SD32 | semidirect |
| 158. C2×Q16 | C2×C3×D3 | semidirect |
| 166. #107 | C2×C3×D3 | semidirect |
| 250. C22×C3 | #828 | semidirect |
| 251. C22×C3 | C3×SD32 | semidirect |
| 273. C32 | #2187 | semidirect |
| 312. C22 | C3×#828 | semidirect |
| 320. C3 | #71085 | direct (N × H) |
| 321. C3 | C3×#2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D24 | 2 |
| C32×#467 | 2 |
| C2×C3×#828 | 2 |
| C3×#4549 | 2 |
| C3×#4491 | 2 |
| C3×#2187 | 3 |
| #71085 | 3 |