Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
227 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 70 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×#364 | C2 | semidirect |
| 3. C3×#4463 | C2 | semidirect |
| 5. #67570 | C3 | direct (N × H) |
| 17. C3×#364 | D3 | semidirect |
| 18. C3×#364 | C2×C3 | semidirect |
| 19. #4463 | C2×C3 | semidirect |
| 65. #364 | C3×D3 | semidirect |
| 176. C32 | #1359 | semidirect |
| 206. C3 | #67570 | direct (N × H) |
| 207. C3 | C3×#1359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4693 | 2 |
| C32×#364 | 2 |
| C3×#4463 | 2 |
| C3×#1359 | 3 |
| #67570 | 3 |