Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
592 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26031564 | C2 | semidirect |
| 3. #26021180 | C2 | semidirect |
| 4. #26021171 | C2 | semidirect |
| 5. #26018751 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 7. C89×#3138 | C2 | semidirect |
| 209. #3138 | D89 | semidirect |
| 214. C89 | #10193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031564 | 2 |
| #26031170 | 2 |
| #26021180 | 2 |
| #26021171 | 2 |
| #26018751 | 2 |
| #26018103 | 2 |
| C89×#3138 | 2 |
| #10193 | 89 |