Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10592774 | C2 | semidirect |
| 3. #10590377 | C2 | semidirect |
| 4. #10590296 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589097 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 36. #4544 | D3 | semidirect |
| 119. C3×C3⋊C8 | SD16 | semidirect |
| 267. C3⋊C8 | #214 | semidirect |
| 332. C32 | #1688 | semidirect |
| 386. C3 | #68413 | semidirect |
| 387. C3 | #71287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592774 | 2 |
| C3×#5073 | 2 |
| #10590377 | 2 |
| #10590296 | 2 |
| C3×#4544 | 2 |
| #10589097 | 2 |
| #10589090 | 2 |
| #71287 | 3 |
| #68413 | 3 |