Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26022002 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151412 | C2 | semidirect |
| 5. #26021981 | C2 | semidirect |
| 6. #26021042 | C2 | semidirect |
| 7. C89×#1378 | C2 | semidirect |
| 55. #15667948 | D4 | semidirect |
| 181. #1378 | D89 | semidirect |
| 182. C89 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030738 | 2 |
| #26022002 | 2 |
| C2×#19151412 | 2 |
| #26021981 | 2 |
| #26021042 | 2 |
| C89×#1378 | 2 |
| #13417 | 89 |