Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
264 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 72 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. C9×#486 | C2 | semidirect |
| 2. #10588769 | C2 | semidirect |
| 4. C8×D36 | C2 | semidirect |
| 5. #10588223 | C2 | semidirect |
| 6. #10588221 | C2 | semidirect |
| 7. #10588134 | C2 | semidirect |
| 87. #486 | D9 | semidirect |
| 200. C9 | #1677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#486 | 2 |
| #10588769 | 2 |
| #10588754 | 2 |
| C8×D36 | 2 |
| #10588223 | 2 |
| #10588221 | 2 |
| #10588134 | 2 |
| #71200 | 3 |