Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26029292 | C2 | semidirect |
| 3. #26020241 | C2 | semidirect |
| 4. #26018920 | C2 | semidirect |
| 5. #26018154 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#1545 | C2 | semidirect |
| 45. C4⋊#10623494 | D4 | semidirect |
| 62. C4⋊C8×C89 | D4 | semidirect |
| 201. #1545 | D89 | semidirect |
| 204. C89 | #9405 | semidirect |
| 254. C4⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029292 | 2 |
| #26025199 | 2 |
| #26020241 | 2 |
| #26018920 | 2 |
| #26018154 | 2 |
| #26018153 | 2 |
| C89×#1545 | 2 |
| #9405 | 89 |