Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26020001 | C2 | semidirect |
| 3. #26018077 | C2 | semidirect |
| 5. C4×C4⋊C8×C89 | C2 | semidirect |
| 173. C4×C4⋊C8 | D89 | semidirect |
| 177. C89 | #7676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028624 | 2 |
| #26020001 | 2 |
| #26018077 | 2 |
| #26018072 | 2 |
| C4×C4⋊C8×C89 | 2 |
| #7676 | 89 |