Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151720 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. #26021126 | 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 |
| 103. Q16×C89 | C22⋊C4 | semidirect |
| 107. D8×C89 | C22⋊C4 | semidirect |
| 181. C2×#360 | D89 | semidirect |
| 185. C89 | #13040 | semidirect |
| 265. Q16 | #13083551 | semidirect |
| 273. D8 | #13083551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| C2×#19151720 | 2 |
| C2×#19151412 | 2 |
| #26021126 | 2 |
| #26018350 | 2 |
| #26018331 | 2 |
| C2×#360×C89 | 2 |
| #13040 | 89 |