Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021027 | C2 | semidirect |
| 2. #26019028 | C2 | semidirect |
| 3. #26019004 | C2 | semidirect |
| 6. #26018126 | C2 | semidirect |
| 165. C89 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021027 | 2 |
| #26019028 | 2 |
| #26019004 | 2 |
| #26018920 | 2 |
| C2×#19151342 | 2 |
| #26018126 | 2 |
| C89×#1965 | 2 |
| #10603 | 89 |