Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×C4×D24 | C2 | semidirect |
| 3. C32×#346 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×#4505 | C2 | semidirect |
| 7. #69078 | C3 | direct (N × H) |
| 15. C3×D48 | C4 | semidirect |
| 19. C4×D24 | C2×C3 | semidirect |
| 23. C3×#346 | D3 | semidirect |
| 24. C3×#346 | C2×C3 | semidirect |
| 25. #4509 | C2×C3 | semidirect |
| 26. #4505 | C2×C3 | semidirect |
| 35. C3×D24 | C2×C4 | semidirect |
| 37. C32×C16 | C2×C4 | semidirect |
| 57. D48 | C3×C4 | semidirect |
| 72. #346 | C3×D3 | semidirect |
| 93. D24 | C2×C3×C4 | semidirect |
| 98. C3×C16 | C4×D3 | semidirect |
| 99. C3×C16 | C2×C3×C4 | semidirect |
| 154. C16 | C3×C4×D3 | semidirect |
| 175. C32 | #2177 | semidirect |
| 203. C3 | #69078 | direct (N × H) |
| 204. C3 | C3×#2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| C3×C4×D24 | 2 |
| C32×#346 | 2 |
| C3×#4509 | 2 |
| C3×#4505 | 2 |
| C3×#2177 | 3 |
| #69078 | 3 |