Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
225 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 74 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×#322 | C2 | semidirect |
| 3. C3×#4463 | C2 | semidirect |
| 5. #67443 | C3 | direct (N × H) |
| 17. C3×#322 | D3 | semidirect |
| 18. C3×#322 | C2×C3 | semidirect |
| 19. #4463 | C2×C3 | semidirect |
| 26. C3×Dic12 | C8 | semidirect |
| 27. C3×D24 | C8 | semidirect |
| 63. #322 | C3×D3 | semidirect |
| 85. Dic12 | C3×C8 | semidirect |
| 86. D24 | C3×C8 | semidirect |
| 167. C32 | #1336 | semidirect |
| 195. C3 | #67443 | direct (N × H) |
| 196. C3 | C3×#1336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4700 | 2 |
| C32×#322 | 2 |
| C3×#4463 | 2 |
| C3×#1336 | 3 |
| #67443 | 3 |