Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4895 | C2 | semidirect |
| 3. C32×#368 | C2 | semidirect |
| 4. C3×Dic3×C16 | C2 | semidirect |
| 5. C3×#4497 | C2 | semidirect |
| 7. #69357 | C3 | direct (N × H) |
| 15. C3×Dic24 | C4 | semidirect |
| 16. C3×#800 | C4 | semidirect |
| 17. C3×D48 | C4 | semidirect |
| 21. #4895 | C2×C3 | semidirect |
| 23. C3×#368 | D3 | semidirect |
| 24. C3×#368 | C2×C3 | semidirect |
| 27. Dic3×C16 | C2×C3 | semidirect |
| 28. #4497 | C2×C3 | semidirect |
| 62. Dic24 | C3×C4 | semidirect |
| 63. #800 | C3×C4 | semidirect |
| 64. D48 | C3×C4 | semidirect |
| 78. #368 | C3×D3 | semidirect |
| 184. C32 | #2178 | semidirect |
| 211. C3 | #69357 | direct (N × H) |
| 212. C3 | C3×#2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| C3×#4895 | 2 |
| C32×#368 | 2 |
| C3×Dic3×C16 | 2 |
| C3×#4497 | 2 |
| C3×#2178 | 3 |
| #69357 | 3 |