Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 4. M16×Dic9 | C2 | semidirect |
| 5. #10588799 | C2 | semidirect |
| 6. #10588209 | C2 | semidirect |
| 7. #10588208 | C2 | semidirect |
| 19. #63394 | C4 | semidirect |
| 20. #63391 | C4 | semidirect |
| 236. C9 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#421 | 2 |
| #10588915 | 2 |
| C2×#63396 | 2 |
| M16×Dic9 | 2 |
| #10588799 | 2 |
| #10588209 | 2 |
| #10588208 | 2 |
| #70401 | 3 |