Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
392 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #10593545 | C2 | semidirect |
| 5. C2×#63746 | C2 | semidirect |
| 6. C2×#63745 | C2 | semidirect |
| 7. #10590090 | C2 | semidirect |
| 200. C32 | #2092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593827 | 2 |
| C2×#63782 | 2 |
| #10593545 | 2 |
| C2×#63746 | 2 |
| C2×#63745 | 2 |
| #10590090 | 2 |
| #2092 | 9 |