Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
694 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 694 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 |
|---|---|---|
| 1. #26029293 | C2 | semidirect |
| 2. #26018643 | C2 | semidirect |
| 3. #26018573 | C2 | semidirect |
| 4. #26018085 | C2 | semidirect |
| 23. C4⋊#10623494 | D4 | semidirect |
| 68. C2×D4×C89 | M16 | semidirect |
| 93. C42×C89 | M16 | semidirect |
| 174. C89 | #8963 | semidirect |
| 234. C2×D4 | #13083558 | semidirect |
| 262. C42 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029293 | 2 |
| #26018643 | 2 |
| #26018573 | 2 |
| #26018085 | 2 |
| C4×#127×C89 | 2 |
| #8963 | 89 |