Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #26025494 | C2 | semidirect |
| 3. #26018135 | C2 | semidirect |
| 4. #26018092 | C2 | semidirect |
| 138. C89 | #10351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025494 | 2 |
| #26021180 | 2 |
| #26018135 | 2 |
| #26018092 | 2 |
| C89×#1957 | 2 |
| #10351 | 89 |