Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26025621 | C2 | semidirect |
| 5. #26018257 | C2 | semidirect |
| 6. #26018197 | C2 | semidirect |
| 7. C89×#1346 | C2 | semidirect |
| 186. #1346 | D89 | semidirect |
| 188. C89 | #12153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025621 | 2 |
| #26021477 | 2 |
| #26019257 | 2 |
| #26019254 | 2 |
| #26018257 | 2 |
| #26018197 | 2 |
| C89×#1346 | 2 |
| #12153 | 89 |