Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. #10588376 | C2 | semidirect |
| 3. #10588376 | C2 | semidirect |
| 4. #10588376 | C2 | semidirect |
| 5. #10588375 | C2 | semidirect |
| 6. #10588361 | C2 | semidirect |
| 7. C9×#322 | C2 | semidirect |
| 85. #322 | D9 | semidirect |
| 182. C9 | #1717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588377 | 2 |
| #10588376 | 2 |
| #10588375 | 2 |
| #10588361 | 2 |
| C9×#322 | 2 |
| #68092 | 3 |