Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
367 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 367 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. C3×#4872 | C2 | semidirect |
| 3. C32×#367 | C2 | semidirect |
| 4. C3×#4502 | C2 | semidirect |
| 5. C3×#4491 | C2 | semidirect |
| 7. #69339 | C3 | direct (N × H) |
| 15. C3×D48 | C4 | semidirect |
| 19. #4872 | C2×C3 | semidirect |
| 21. C3×#367 | D3 | semidirect |
| 22. C3×#367 | C2×C3 | semidirect |
| 25. #4502 | C2×C3 | semidirect |
| 26. #4491 | C2×C3 | semidirect |
| 35. C3×D24 | C2×C4 | semidirect |
| 36. C32×C16 | C2×C4 | semidirect |
| 56. D48 | C3×C4 | semidirect |
| 69. #367 | C3×D3 | semidirect |
| 91. D24 | C2×C3×C4 | semidirect |
| 94. C3×C16 | C4×D3 | semidirect |
| 95. C3×C16 | C2×C3×C4 | semidirect |
| 150. C16 | C3×C4×D3 | semidirect |
| 171. C32 | #2177 | semidirect |
| 199. C3 | #69339 | direct (N × H) |
| 200. 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×#4872 | 2 |
| C32×#367 | 2 |
| C3×#4502 | 2 |
| C3×#4491 | 2 |
| C3×#2177 | 3 |
| #69339 | 3 |