Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10588627 | C2 | semidirect |
| 3. #10588405 | C2 | semidirect |
| 4. #10588404 | C2 | semidirect |
| 5. C9×#323 | C2 | semidirect |
| 6. #10588147 | C2 | semidirect |
| 7. #10588144 | C2 | semidirect |
| 126. #323 | D9 | semidirect |
| 291. C9 | #1606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589596 | 2 |
| #10588627 | 2 |
| #10588405 | 2 |
| #10588404 | 2 |
| C9×#323 | 2 |
| #10588147 | 2 |
| #10588144 | 2 |
| #68109 | 3 |