Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26018196 | C2 | semidirect |
| 4. #26018186 | C2 | semidirect |
| 172. C89 | #11551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018582 | 2 |
| C2×#19151324 | 2 |
| #26018196 | 2 |
| #26018186 | 2 |
| C89×#2503 | 2 |
| #11551 | 89 |