Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 94 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. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 3. C3×#5021 | C2 | semidirect |
| 5. #10589098 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 33. #5021 | D3 | semidirect |
| 292. C32 | #1678 | semidirect |
| 337. C3 | #71022 | semidirect |
| 338. C3 | #71150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊C8) | 2 |
| C3×#5027 | 2 |
| C3×#5021 | 2 |
| #10590277 | 2 |
| #10589098 | 2 |
| #10589095 | 2 |
| #10589090 | 2 |
| #71150 | 3 |
| #71022 | 3 |