Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
785 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 785 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 1. C2×C3×#904 | C2 | semidirect |
| 2. C22×C3⋊(C3⋊C16) | C2 | semidirect |
| 3. C2×#63550 | C2 | semidirect |
| 4. C2×#63547 | C2 | semidirect |
| 5. #10590629 | C2 | direct (N × H) |
| 6. C2×#63545 | C2 | semidirect |
| 12. C3×#904 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 18. #63550 | C22 | semidirect |
| 19. #63547 | C22 | semidirect |
| 20. #63545 | C22 | semidirect |
| 22. C2×#904 | D3 | semidirect |
| 60. #904 | C2×D3 | semidirect |
| 186. C2×C32 | #508 | semidirect |
| 225. C32 | C2×#508 | semidirect |
| 247. C2×C3 | #5194 | semidirect |
| 260. C3 | C2×#5194 | semidirect |
| 263. C2 | #10590629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#904 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| C2×#63550 | 2 |
| C2×#63547 | 2 |
| #10590629 | 2 |
| C2×#63545 | 2 |
| C2×#5194 | 3 |