Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
894 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 115 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×#19151388 | C2 | semidirect |
| 4. #26018370 | C2 | semidirect |
| 15. C2×#123×C89 | C4 | semidirect |
| 17. C22×C22⋊C4×C89 | C4 | semidirect |
| 20. #386×C89 | C4 | semidirect |
| 24. #379×C89 | C4 | semidirect |
| 50. C23×C4×C89 | C2×C4 | semidirect |
| 51. C23×C4×C89 | C2×C4 | semidirect |
| 68. C2×C22⋊C4×C89 | C2×C4 | semidirect |
| 69. C2×C22⋊C4×C89 | C2×C4 | semidirect |
| 264. C22×C89 | #352 | semidirect |
| 293. C89 | #13084 | semidirect |
| 295. C2×#123 | Dic89 | semidirect |
| 298. C22×C22⋊C4 | Dic89 | semidirect |
| 307. #386 | Dic89 | semidirect |
| 311. #379 | Dic89 | semidirect |
| 325. C23×C4 | C2×Dic89 | semidirect |
| 326. C23×C4 | C2×Dic89 | semidirect |
| 348. C2×C22⋊C4 | C2×Dic89 | semidirect |
| 349. C2×C22⋊C4 | C2×Dic89 | semidirect |
| 552. C22 | #19151388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667927 | 2 |
| C2×#19151388 | 2 |
| #26020173 | 2 |
| #26018370 | 2 |
| C89×#2405 | 2 |
| #13084 | 89 |