Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#19151418 | C2 | semidirect |
| 5. #26020415 | C2 | semidirect |
| 6. #26018362 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 12. #19151714 | C4 | semidirect |
| 163. #1387 | D89 | semidirect |
| 164. C89 | #12820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151714 | 2 |
| C2×#19151418 | 2 |
| #26021965 | 2 |
| #26021962 | 2 |
| #26020415 | 2 |
| #26018362 | 2 |
| C89×#1387 | 2 |
| #12820 | 89 |