Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 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. #26019011 | C2 | semidirect |
| 3. #26018217 | C2 | semidirect |
| 4. #26018214 | C2 | semidirect |
| 5. C89×#2162 | C2 | semidirect |
| 65. Dic356 | M16 | semidirect |
| 68. D712 | M16 | semidirect |
| 152. #2162 | D89 | semidirect |
| 156. C89 | #11660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668034 | 2 |
| #26019011 | 2 |
| #26018217 | 2 |
| #26018214 | 2 |
| C89×#2162 | 2 |
| #11660 | 89 |