Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26018998 | C2 | semidirect |
| 3. C2×#19151348 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 7. C89×#1283 | C2 | semidirect |
| 161. #1283 | D89 | semidirect |
| 162. C89 | #8607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028897 | 2 |
| #26018998 | 2 |
| C2×#19151348 | 2 |
| #26018640 | 2 |
| #26018637 | 2 |
| #26018103 | 2 |
| C89×#1283 | 2 |
| #8607 | 89 |