Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
164 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 25 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. #26018419 | C2 | semidirect |
| 3. C89×#1409 | C2 | semidirect |
| 4. #19151975 | C4 | semidirect |
| 8. #19151319 | C4 | semidirect |
| 69. #1409 | D89 | semidirect |
| 70. C89 | #7527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019916 | 2 |
| #26018419 | 2 |
| C89×#1409 | 2 |
| #7527 | 89 |