Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#15667956 | C2 | semidirect |
| 3. #26029908 | C2 | semidirect |
| 4. C2×#19151415 | C2 | semidirect |
| 5. C2×#19151383 | C2 | semidirect |
| 6. #26018347 | C2 | semidirect |
| 7. C89×#2140 | C2 | semidirect |
| 198. #2140 | D89 | semidirect |
| 201. C89 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667956 | 2 |
| C2×#19151865 | 2 |
| #26029908 | 2 |
| C2×#19151415 | 2 |
| C2×#19151383 | 2 |
| #26018347 | 2 |
| C89×#2140 | 2 |
| #13320 | 89 |