Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
712 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #26018276 | C2 | direct (N × H) |
| 12. C22×C4⋊C4×C89 | C4 | semidirect |
| 17. #399×C89 | C4 | semidirect |
| 19. C2×#95×C89 | C4 | semidirect |
| 39. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 50. #95×C89 | C2×C4 | semidirect |
| 197. C2×C89 | #1352 | semidirect |
| 205. C89 | C2×#1352 | semidirect |
| 207. C22×C4⋊C4 | Dic89 | semidirect |
| 214. #399 | Dic89 | semidirect |
| 216. C2×#95 | Dic89 | semidirect |
| 234. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 251. #95 | C2×Dic89 | semidirect |
| 397. C2 | #26018276 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151365 | 2 |
| C2×#19151322 | 2 |
| #26018276 | 2 |
| C2×#399×C89 | 2 |
| C2×#1352 | 89 |