Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26027931 | C2 | semidirect |
| 2. #26021478 | C2 | semidirect |
| 4. #26018279 | C2 | semidirect |
| 5. #26018256 | C2 | semidirect |
| 6. #26018195 | C2 | semidirect |
| 7. C89×#1616 | C2 | semidirect |
| 194. #1616 | D89 | semidirect |
| 199. C89 | #12141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027931 | 2 |
| #26021478 | 2 |
| #26019187 | 2 |
| #26018279 | 2 |
| #26018256 | 2 |
| #26018195 | 2 |
| C89×#1616 | 2 |
| #12141 | 89 |