Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #26018196 | C2 | semidirect |
| 5. #26018185 | C2 | semidirect |
| 6. #26018185 | C2 | semidirect |
| 7. C89×#1324 | C2 | semidirect |
| 189. #1324 | D89 | semidirect |
| 192. C89 | #11551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024734 | 2 |
| #26018580 | 2 |
| #324×D89 | 2 |
| #26018196 | 2 |
| #26018185 | 2 |
| C89×#1324 | 2 |
| #11551 | 89 |