Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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×#63381 | C2 | semidirect |
| 5. C2×#63366 | C2 | semidirect |
| 6. C9×#343 | C2 | semidirect |
| 7. #10588234 | C2 | semidirect |
| 17. #63469 | C4 | semidirect |
| 115. #343 | D9 | semidirect |
| 256. C9 | #1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63469 | 2 |
| #10588815 | 2 |
| C2×#63381 | 2 |
| #10588649 | 2 |
| C2×#63366 | 2 |
| C9×#343 | 2 |
| #10588234 | 2 |
| #69001 | 3 |