Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
824 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19151367 | C2 | semidirect |
| 3. #26018256 | C2 | direct (N × H) |
| 4. C2×#324×C89 | C2 | semidirect |
| 15. #19151367 | C22 | semidirect |
| 19. #324×C89 | C22 | semidirect |
| 197. C2×C89 | #1345 | semidirect |
| 204. C2×#324 | D89 | semidirect |
| 206. C89 | C2×#1345 | semidirect |
| 221. #324 | C2×D89 | semidirect |
| 399. C2 | #26018256 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151515 | 2 |
| C2×#19151367 | 2 |
| #26018256 | 2 |
| C2×#324×C89 | 2 |
| C2×#1345 | 89 |