Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 558 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 |
|---|---|---|
| 1. C2×#19152041 | C2 | semidirect |
| 2. C2×#19152038 | C2 | semidirect |
| 4. C2×#19151407 | C2 | semidirect |
| 5. #26021121 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 47. C2×Dic356 | D4 | semidirect |
| 67. #15667952 | D4 | semidirect |
| 84. M32×C89 | D4 | semidirect |
| 225. C2×#360 | D89 | semidirect |
| 228. C89 | #13342 | semidirect |
| 300. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| C2×#19152038 | 2 |
| #26030695 | 2 |
| C2×#19151407 | 2 |
| #26021121 | 2 |
| #26018335 | 2 |
| C2×#360×C89 | 2 |
| #13342 | 89 |