Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 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×#19151420 | C2 | semidirect |
| 4. #26020978 | C2 | semidirect |
| 5. #26018351 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 18. #19151408 | C4 | semidirect |
| 87. Q16×C89 | C4⋊C4 | semidirect |
| 91. D8×C89 | C4⋊C4 | semidirect |
| 164. C89 | #12950 | semidirect |
| 229. Q16 | #13083553 | semidirect |
| 233. D8 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151715 | 2 |
| C2×#19151420 | 2 |
| C2×#19151408 | 2 |
| #26020978 | 2 |
| #26018351 | 2 |
| #26018333 | 2 |
| C2×#360×C89 | 2 |
| #12950 | 89 |