Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 99 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. C4×#15667947 | C2 | semidirect |
| 3. #26018843 | C2 | semidirect |
| 4. #26018670 | C2 | semidirect |
| 5. #26018669 | C2 | semidirect |
| 6. M16×#10623494 | C2 | semidirect |
| 7. C89×#1525 | C2 | semidirect |
| 187. #1525 | D89 | semidirect |
| 191. C89 | #9724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030827 | 2 |
| C4×#15667947 | 2 |
| #26018843 | 2 |
| #26018670 | 2 |
| #26018669 | 2 |
| M16×#10623494 | 2 |
| C89×#1525 | 2 |
| #9724 | 89 |