Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 4. C2×#19151403 | C2 | semidirect |
| 5. #26021167 | C2 | semidirect |
| 6. #26018361 | C2 | semidirect |
| 7. C89×#1379 | C2 | semidirect |
| 12. #19152041 | C4 | semidirect |
| 39. C2×Dic356 | C2×C4 | semidirect |
| 65. M32×C89 | C2×C4 | semidirect |
| 188. #1379 | D89 | semidirect |
| 189. C89 | #13023 | semidirect |
| 238. M32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| #26029129 | 2 |
| C2×#19151406 | 2 |
| C2×#19151403 | 2 |
| #26021167 | 2 |
| #26018361 | 2 |
| C89×#1379 | 2 |
| #13023 | 89 |