Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26019276 | C2 | semidirect |
| 3. #26019208 | C2 | semidirect |
| 4. #26018276 | C2 | semidirect |
| 5. #26018273 | C2 | semidirect |
| 88. C24×C89 | Q16 | semidirect |
| 224. C89 | #12214 | semidirect |
| 287. C24 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021416 | 2 |
| #26019276 | 2 |
| #26019208 | 2 |
| #26018276 | 2 |
| #26018273 | 2 |
| #26018180 | 2 |
| C89×#2437 | 2 |
| #12214 | 89 |