Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26030697 | C2 | semidirect |
| 2. #26030252 | C2 | semidirect |
| 3. #26021051 | C2 | semidirect |
| 4. #26018652 | C2 | semidirect |
| 5. #26018651 | C2 | semidirect |
| 6. #26018082 | C2 | semidirect |
| 7. C89×#3100 | C2 | semidirect |
| 103. C2×#10623494 | D8 | semidirect |
| 224. #3100 | D89 | semidirect |
| 229. C89 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030697 | 2 |
| #26030252 | 2 |
| #26021051 | 2 |
| #26018652 | 2 |
| #26018651 | 2 |
| #26018082 | 2 |
| C89×#3100 | 2 |
| #10032 | 89 |