Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #26020973 | C2 | semidirect |
| 5. #26018153 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1570 | C2 | semidirect |
| 167. #1570 | D89 | semidirect |
| 172. C89 | #8880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028969 | 2 |
| #26020973 | 2 |
| #26018748 | 2 |
| #26018650 | 2 |
| #26018153 | 2 |
| #26018096 | 2 |
| C89×#1570 | 2 |
| #8880 | 89 |