Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26018368 | C2 | semidirect |
| 5. #26018363 | C2 | semidirect |
| 6. #26018338 | C2 | semidirect |
| 7. C89×#1833 | C2 | semidirect |
| 132. #1833 | D89 | semidirect |
| 136. C89 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151410 | 2 |
| #26021967 | 2 |
| #26021162 | 2 |
| #26018368 | 2 |
| #26018363 | 2 |
| #26018338 | 2 |
| C89×#1833 | 2 |
| #13490 | 89 |