Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26025913 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 34. C22×Dic178 | Q8 | semidirect |
| 35. C22×D356 | Q8 | semidirect |
| 253. #1284 | D89 | semidirect |
| 254. C89 | #10386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025913 | 2 |
| #26020197 | 2 |
| #26020195 | 2 |
| #26020169 | 2 |
| #26018161 | 2 |
| #26018104 | 2 |
| C89×#1284 | 2 |
| #10386 | 89 |