Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 321 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 |
|---|---|---|
| 1. C2×#63656 | C2 | semidirect |
| 5. C3×#4565 | C2 | semidirect |
| 6. #10589144 | C2 | semidirect |
| 7. #10589131 | C2 | semidirect |
| 35. #4565 | D3 | semidirect |
| 273. C32 | #2222 | semidirect |
| 306. C3 | #69270 | semidirect |
| 307. C3 | #71096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63656 | 2 |
| C3×#5192 | 2 |
| #10590932 | 2 |
| #10590622 | 2 |
| C3×#4565 | 2 |
| #10589144 | 2 |
| #10589131 | 2 |
| #71096 | 3 |
| #69270 | 3 |