Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
480 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. C2×#19151356 | C2 | semidirect |
| 3. #26018244 | C2 | direct (N × H) |
| 4. C2×#349×C89 | C2 | semidirect |
| 15. #19151356 | C22 | semidirect |
| 19. #349×C89 | C22 | semidirect |
| 172. C2×C89 | #1341 | semidirect |
| 176. C2×#349 | D89 | semidirect |
| 179. C89 | C2×#1341 | semidirect |
| 192. #349 | C2×D89 | semidirect |
| 347. C2 | #26018244 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151851 | 2 |
| C2×#19151356 | 2 |
| #26018244 | 2 |
| C2×#349×C89 | 2 |
| C2×#1341 | 89 |