Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
342 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 80 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. C9×#477 | C2 | semidirect |
| 4. #10588759 | C2 | semidirect |
| 5. #10588212 | C2 | semidirect |
| 7. #10588159 | C2 | semidirect |
| 100. #477 | D9 | semidirect |
| 225. C9 | #1637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D36 | 2 |
| C9×#477 | 2 |
| #10588769 | 2 |
| #10588759 | 2 |
| #10588212 | 2 |
| #10588162 | 2 |
| #10588159 | 2 |
| #71163 | 3 |