Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. #10589774 | C2 | semidirect |
| 3. #10588751 | C2 | semidirect |
| 4. #10588217 | C2 | semidirect |
| 5. #10588141 | C2 | semidirect |
| 173. C9 | #1657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589774 | 2 |
| C9×#496 | 2 |
| #10588751 | 2 |
| #10588217 | 2 |
| #10588141 | 2 |
| #71328 | 3 |