Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1382 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×#15667931 | C2 | semidirect |
| 3. C2×#19151394 | C2 | direct (N × H) |
| 4. C22×#101×C89 | C2 | semidirect |
| 15. C2×#15667931 | C22 | semidirect |
| 16. #19151394 | C22 | direct (N × H) |
| 20. C2×#101×C89 | C22 | semidirect |
| 42. #15667931 | C23 | semidirect |
| 56. #101×C89 | C23 | semidirect |
| 148. C22×C89 | #355 | semidirect |
| 166. C2×C89 | C2×#355 | semidirect |
| 171. C22×#101 | D89 | semidirect |
| 173. C89 | C22×#355 | semidirect |
| 188. C2×#101 | C2×D89 | semidirect |
| 225. #101 | C22×D89 | semidirect |
| 321. C22 | #19151394 | direct (N × H) |
| 335. C2 | C2×#19151394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668001 | 2 |
| C22×#15667931 | 2 |
| C2×#19151394 | 2 |
| C22×#101×C89 | 2 |
| C22×#355 | 89 |