Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
910 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 910 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26031027 | C2 | semidirect |
| 3. #26018825 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 78. C24×C89 | Q16 | semidirect |
| 196. C89 | #10324 | semidirect |
| 250. C24 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031027 | 2 |
| #26028539 | 2 |
| #26018825 | 2 |
| #26018120 | 2 |
| C89×#1779 | 2 |
| #10324 | 89 |