Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 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 |
|---|---|---|
| 3. C2×#19151415 | C2 | semidirect |
| 5. #26021113 | C2 | semidirect |
| 6. #26018361 | C2 | semidirect |
| 7. C89×#1376 | C2 | semidirect |
| 12. #19152041 | C4 | semidirect |
| 184. #1376 | 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×#19151716 | 2 |
| C2×#19151415 | 2 |
| #26021965 | 2 |
| #26021113 | 2 |
| #26018361 | 2 |
| C89×#1376 | 2 |
| #13028 | 89 |