Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#19151415 | C2 | semidirect |
| 4. C2×#19151401 | C2 | semidirect |
| 6. #26018345 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 17. #19151874 | C4 | semidirect |
| 176. #1387 | D89 | semidirect |
| 178. C89 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152016 | 2 |
| C2×#19151874 | 2 |
| C2×#19151415 | 2 |
| C2×#19151401 | 2 |
| #26020317 | 2 |
| #26018345 | 2 |
| C89×#1387 | 2 |
| #13072 | 89 |