Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19151978 | C2 | semidirect |
| 3. C2×#19151403 | C2 | semidirect |
| 5. C89×#1374 | C2 | semidirect |
| 96. C2×C4×C89 | SD32 | semidirect |
| 147. #1374 | D89 | semidirect |
| 148. C89 | #13327 | semidirect |
| 252. C2×C4 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667957 | 2 |
| C2×#19151978 | 2 |
| C2×#19151403 | 2 |
| #26021118 | 2 |
| C89×#1374 | 2 |
| #13327 | 89 |