Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
538 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19151709 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. #26021146 | C2 | semidirect |
| 5. #26018350 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 12. C2×#15667955 | C4 | semidirect |
| 13. C2×#15667953 | C4 | semidirect |
| 45. C2×#13083549 | C2×C4 | semidirect |
| 58. C2×Q16×C89 | C2×C4 | semidirect |
| 60. C2×D8×C89 | C2×C4 | semidirect |
| 182. C2×#360 | D89 | semidirect |
| 186. C89 | #13037 | semidirect |
| 213. C2×Q16 | C4×D89 | semidirect |
| 221. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| C2×#19151709 | 2 |
| C2×#19151412 | 2 |
| #26021146 | 2 |
| #26018350 | 2 |
| #26018331 | 2 |
| C2×#360×C89 | 2 |
| #13037 | 89 |