Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26028860 | C2 | semidirect |
| 3. #26021979 | C2 | semidirect |
| 4. C2×#19151406 | C2 | semidirect |
| 5. C2×#19151381 | C2 | semidirect |
| 6. #26018365 | C2 | semidirect |
| 7. C89×#1381 | C2 | semidirect |
| 185. #1381 | D89 | semidirect |
| 186. C89 | #12995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029973 | 2 |
| #26028860 | 2 |
| #26021979 | 2 |
| C2×#19151406 | 2 |
| C2×#19151381 | 2 |
| #26018365 | 2 |
| C89×#1381 | 2 |
| #12995 | 89 |