Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
592 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 592 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 |
|---|---|---|
| 3. #26018276 | C2 | semidirect |
| 4. #26018273 | C2 | semidirect |
| 12. C2×C22⋊Q8×C89 | C4 | semidirect |
| 14. #399×C89 | C4 | semidirect |
| 18. #393×C89 | C4 | semidirect |
| 21. #380×C89 | C4 | semidirect |
| 32. C22×Q8×C89 | C2×C4 | semidirect |
| 41. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 56. #95×C89 | C2×C4 | semidirect |
| 57. #95×C89 | C2×C4 | semidirect |
| 222. C89 | #11716 | semidirect |
| 223. C2×C22⋊Q8 | Dic89 | semidirect |
| 227. #399 | Dic89 | semidirect |
| 231. #393 | Dic89 | semidirect |
| 234. #380 | Dic89 | semidirect |
| 241. C22×Q8 | C2×Dic89 | semidirect |
| 252. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 273. #95 | C2×Dic89 | semidirect |
| 274. #95 | C2×Dic89 | semidirect |
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 |
| #26018273 | 2 |
| C89×#2626 | 2 |
| #11716 | 89 |