Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #26018533 | C2 | semidirect |
| 5. M16×#10623494 | C2 | semidirect |
| 6. #26018141 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 154. #1299 | D89 | semidirect |
| 155. C89 | #8241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028963 | 2 |
| #26018912 | 2 |
| #26018843 | 2 |
| #26018533 | 2 |
| M16×#10623494 | 2 |
| #26018141 | 2 |
| C89×#1299 | 2 |
| #8241 | 89 |