Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 51. C22×Q8×C89 | Q8 | semidirect |
| 59. C2×C4⋊C4×C89 | Q8 | semidirect |
| 218. C89 | #10375 | semidirect |
| 239. C22×Q8 | Dic178 | semidirect |
| 258. C2×C4⋊C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025258 | 2 |
| #26018824 | 2 |
| C2×#19151335 | 2 |
| #26018130 | 2 |
| #26018119 | 2 |
| #26018100 | 2 |
| C89×#1996 | 2 |
| #10375 | 89 |