Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
543 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 104 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×#63431 | C2 | semidirect |
| 4. C2×#63382 | C2 | semidirect |
| 5. #10588681 | C2 | semidirect |
| 7. C9×#339 | C2 | semidirect |
| 141. #339 | D9 | semidirect |
| 314. C9 | #2005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63471 | 2 |
| #10589628 | 2 |
| C2×#63431 | 2 |
| C2×#63382 | 2 |
| #10588681 | 2 |
| C2×#63364 | 2 |
| C9×#339 | 2 |
| #68768 | 3 |