Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. C2×#19151413 | C2 | semidirect |
| 5. #26021111 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 12. #19152041 | C4 | semidirect |
| 183. #1387 | D89 | semidirect |
| 185. C89 | #13028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| C2×#19151714 | 2 |
| C2×#19151413 | 2 |
| #26021962 | 2 |
| #26021111 | 2 |
| #26018333 | 2 |
| C89×#1387 | 2 |
| #13028 | 89 |