Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26025258 | C2 | semidirect |
| 5. #26018132 | C2 | semidirect |
| 6. #26018120 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 28. C22×D356 | Q8 | semidirect |
| 42. C2×C4⋊Dic89 | Q8 | semidirect |
| 236. #1282 | D89 | semidirect |
| 237. C89 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025258 | 2 |
| #26021088 | 2 |
| #26018821 | 2 |
| C2×#19151333 | 2 |
| #26018132 | 2 |
| #26018120 | 2 |
| C89×#1282 | 2 |
| #10374 | 89 |