Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1164 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1164 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×#19151322 | C2 | semidirect |
| 3. #26018248 | C2 | direct (N × H) |
| 4. C2×#342×C89 | C2 | semidirect |
| 5. C23×D356 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 13. C2×#15667919 | C4 | semidirect |
| 15. #19151322 | C22 | semidirect |
| 19. #342×C89 | C22 | semidirect |
| 25. C22×D356 | C2×C4 | semidirect |
| 40. #15667919 | C2×C4 | semidirect |
| 243. C2×C89 | #1343 | semidirect |
| 249. C2×#342 | D89 | semidirect |
| 252. C89 | C2×#1343 | semidirect |
| 265. #342 | C2×D89 | semidirect |
| 491. C2 | #26018248 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151507 | 2 |
| C2×#19151322 | 2 |
| #26018248 | 2 |
| C2×#342×C89 | 2 |
| C2×#1343 | 89 |