Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
328 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 97 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×#19151375 | C2 | semidirect |
| 5. #26020991 | C2 | semidirect |
| 6. #26018352 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 16. #19151401 | C4 | semidirect |
| 17. #19151398 | C4 | semidirect |
| 154. #1387 | D89 | semidirect |
| 156. C89 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151409 | 2 |
| #26021962 | 2 |
| C2×#19151375 | 2 |
| #26021143 | 2 |
| #26020991 | 2 |
| #26018352 | 2 |
| C89×#1387 | 2 |
| #13153 | 89 |