Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021205 | C2 | semidirect |
| 4. #26019004 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#1966 | C2 | semidirect |
| 193. #1966 | D89 | semidirect |
| 197. C89 | #10503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031373 | 2 |
| #26021205 | 2 |
| #26021171 | 2 |
| #26019004 | 2 |
| #26018930 | 2 |
| #26018153 | 2 |
| C89×#1966 | 2 |
| #10503 | 89 |