Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 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×#19151715 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. #26021116 | C2 | semidirect |
| 5. #26018360 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C89×#2139 | C2 | semidirect |
| 11. #19152033 | C4 | semidirect |
| 106. Q16×C89 | C22⋊C4 | semidirect |
| 110. D8×C89 | C22⋊C4 | semidirect |
| 189. #2139 | D89 | semidirect |
| 193. C89 | #13029 | semidirect |
| 275. Q16 | #13083551 | semidirect |
| 283. 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×#19151715 | 2 |
| C2×#19151412 | 2 |
| #26021116 | 2 |
| #26018360 | 2 |
| #26018333 | 2 |
| C89×#2139 | 2 |
| #13029 | 89 |