Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
429 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 110 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. C2×C3×#827 | C2 | semidirect |
| 3. C3×C4×Dic12 | C2 | semidirect |
| 4. C3×#4562 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 7. #71294 | C3 | direct (N × H) |
| 23. C2×#827 | C2×C3 | semidirect |
| 24. C4×Dic12 | C2×C3 | semidirect |
| 27. #4562 | C2×C3 | semidirect |
| 28. C4⋊(C3⋊C16) | C2×C3 | semidirect |
| 43. C3×Dic12 | D4 | semidirect |
| 128. Dic12 | C3×D4 | semidirect |
| 136. C32×C4 | SD32 | semidirect |
| 232. C3×C4 | #827 | semidirect |
| 233. C3×C4 | C3×SD32 | semidirect |
| 240. C32 | #2207 | semidirect |
| 275. C4 | C3×#827 | semidirect |
| 279. C3 | #71294 | direct (N × H) |
| 280. C3 | C3×#2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C2×C3×#827 | 2 |
| C3×C4×Dic12 | 2 |
| C3×#4562 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#2207 | 3 |
| #71294 | 3 |