Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. C2×#63382 | C2 | semidirect |
| 4. C2×#63381 | C2 | semidirect |
| 6. C2×#63368 | C2 | semidirect |
| 7. C9×#343 | C2 | semidirect |
| 120. #343 | D9 | semidirect |
| 270. C9 | #2052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63471 | 2 |
| #10588811 | 2 |
| C2×#63382 | 2 |
| C2×#63381 | 2 |
| #10588649 | 2 |
| C2×#63368 | 2 |
| C9×#343 | 2 |
| #68987 | 3 |