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×#19151402 | C2 | semidirect |
| 4. #26018330 | C2 | semidirect |
| 5. C2×#494×C89 | C2 | semidirect |
| 103. C2×C4×C89 | SD32 | semidirect |
| 144. C2×#494 | D89 | semidirect |
| 148. C89 | #13327 | semidirect |
| 252. C2×C4 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| C2×#19151402 | 2 |
| #26021118 | 2 |
| #26018330 | 2 |
| C2×#494×C89 | 2 |
| #13327 | 89 |