Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 594 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. #26025919 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 252. #1284 | D89 | semidirect |
| 253. C89 | #10388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025919 | 2 |
| #26020197 | 2 |
| #26020195 | 2 |
| #26020169 | 2 |
| #26018161 | 2 |
| #26018104 | 2 |
| C89×#1284 | 2 |
| #10388 | 89 |