Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
704 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26027282 | C2 | semidirect |
| 3. C2×#19151397 | C2 | semidirect |
| 4. C2×#19151396 | C2 | semidirect |
| 6. #26018378 | C2 | semidirect |
| 275. C89 | #13359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151781 | 2 |
| #26027282 | 2 |
| C2×#19151397 | 2 |
| C2×#19151396 | 2 |
| #26020211 | 2 |
| #26018378 | 2 |
| C2×#456×C89 | 2 |
| #13359 | 89 |