Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26033354 | C2 | semidirect |
| 3. #26021969 | C2 | semidirect |
| 4. #26021967 | C2 | semidirect |
| 5. #26020295 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#1384 | C2 | semidirect |
| 15. #19151852 | C4 | semidirect |
| 49. C2×#13083549 | D4 | semidirect |
| 60. C2×C16×C89 | D4 | semidirect |
| 176. #1384 | D89 | semidirect |
| 177. C89 | #13074 | semidirect |
| 226. C2×C16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029901 | 2 |
| #26021969 | 2 |
| #26021967 | 2 |
| #26020295 | 2 |
| #26018353 | 2 |
| C89×#1384 | 2 |
| #13074 | 89 |