Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
484 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26028524 | C2 | semidirect |
| 4. #26018134 | C2 | semidirect |
| 5. C89×#1295 | C2 | semidirect |
| 25. #15668009 | Q8 | semidirect |
| 147. #1295 | D89 | semidirect |
| 148. C89 | #10358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028524 | 2 |
| #26021076 | 2 |
| #26021075 | 2 |
| #26018134 | 2 |
| C89×#1295 | 2 |
| #10358 | 89 |