Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. C2×#19151415 | C2 | semidirect |
| 5. #26021113 | C2 | semidirect |
| 6. #26018361 | C2 | semidirect |
| 7. C2×#364×C89 | C2 | semidirect |
| 170. C2×#364 | D89 | semidirect |
| 176. C89 | #13446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| C2×#19151415 | 2 |
| #26021965 | 2 |
| #26021140 | 2 |
| #26021113 | 2 |
| #26018361 | 2 |
| C2×#364×C89 | 2 |
| #13446 | 89 |