Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26018647 | C2 | semidirect |
| 4. #26018085 | C2 | semidirect |
| 59. C2×Q8×C89 | M16 | semidirect |
| 87. C42×C89 | M16 | semidirect |
| 158. C89 | #8961 | semidirect |
| 209. C2×Q8 | #13083558 | semidirect |
| 240. C42 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| #26018647 | 2 |
| #26018573 | 2 |
| #26018085 | 2 |
| C4×#124×C89 | 2 |
| #8961 | 89 |