Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
342 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 1. C9×#424 | C2 | semidirect |
| 4. C2×#63372 | C2 | semidirect |
| 6. #10588679 | C2 | semidirect |
| 7. #10588234 | C2 | semidirect |
| 100. #424 | D9 | semidirect |
| 238. C9 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#424 | 2 |
| C2×#63383 | 2 |
| C2×#63380 | 2 |
| C2×#63372 | 2 |
| #10588682 | 2 |
| #10588679 | 2 |
| #10588234 | 2 |
| #70542 | 3 |