Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26019991 | C2 | semidirect |
| 3. #26018256 | C2 | semidirect |
| 4. C89×#1458 | C2 | semidirect |
| 174. #1458 | D89 | semidirect |
| 176. C89 | #11699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026002 | 2 |
| #26019991 | 2 |
| #26018256 | 2 |
| C89×#1458 | 2 |
| #11699 | 89 |