Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 94 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×#510 | C2 | semidirect |
| 3. C3×#5192 | C2 | semidirect |
| 4. C2×C3×#828 | C2 | semidirect |
| 5. C3×#4567 | C2 | semidirect |
| 6. C3×#4516 | C2 | semidirect |
| 7. C3×#4515 | C2 | semidirect |
| 9. #71523 | C3 | direct (N × H) |
| 12. C2×C32×Q16 | C22 | semidirect |
| 22. C32×M32 | C22 | semidirect |
| 25. C3×#819 | C22 | semidirect |
| 26. C2×C3×C3⋊C16 | C22 | semidirect |
| 30. C3×#510 | D3 | semidirect |
| 31. C3×#510 | C2×C3 | semidirect |
| 34. #5192 | C2×C3 | semidirect |
| 35. C2×#828 | C2×C3 | semidirect |
| 39. #4567 | C2×C3 | semidirect |
| 40. #4516 | C2×C3 | semidirect |
| 41. #4515 | C2×C3 | semidirect |
| 80. C2×C3×Q16 | C2×D3 | semidirect |
| 81. C2×C3×Q16 | C22×C3 | semidirect |
| 100. C3×M32 | C2×D3 | semidirect |
| 101. C3×M32 | C22×C3 | semidirect |
| 107. #819 | C22×C3 | semidirect |
| 108. C2×C3⋊C16 | C22×C3 | semidirect |
| 133. #510 | C3×D3 | semidirect |
| 219. C2×Q16 | C2×C3×D3 | semidirect |
| 226. M32 | C2×C3×D3 | semidirect |
| 346. C32 | #2194 | semidirect |
| 395. C3 | #71523 | direct (N × H) |
| 396. C3 | C3×#2194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5769 | 2 |
| C32×#510 | 2 |
| C3×#5192 | 2 |
| C2×C3×#828 | 2 |
| C3×#4567 | 2 |
| C3×#4516 | 2 |
| C3×#4515 | 2 |
| C3×#2194 | 3 |
| #71523 | 3 |