Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#63656 | C2 | semidirect |
| 5. #10589431 | C2 | semidirect |
| 6. #10589362 | C2 | semidirect |
| 7. #10589359 | C2 | semidirect |
| 178. C32 | #2222 | semidirect |
| 205. C3 | #71096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#473 | 2 |
| C2×#63656 | 2 |
| #10592842 | 2 |
| #10592839 | 2 |
| #10589431 | 2 |
| #10589362 | 2 |
| #10589359 | 2 |
| #71096 | 3 |