Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10588386 | C2 | semidirect |
| 3. D9×#97 | C2 | semidirect |
| 4. C9×#329 | C2 | semidirect |
| 5. #10588217 | C2 | semidirect |
| 6. #10588142 | C2 | semidirect |
| 7. #10588142 | C2 | semidirect |
| 119. #329 | D9 | semidirect |
| 269. C9 | #1530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589770 | 2 |
| #10588386 | 2 |
| D9×#97 | 2 |
| C9×#329 | 2 |
| #10588217 | 2 |
| #10588142 | 2 |
| #68345 | 3 |