Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26031562 | C2 | semidirect |
| 2. #26022164 | C2 | semidirect |
| 3. #26018260 | C2 | semidirect |
| 4. #26018192 | C2 | semidirect |
| 5. C89×#2054 | C2 | semidirect |
| 106. C2×C4×C89 | D16 | semidirect |
| 152. #2054 | D89 | semidirect |
| 155. C89 | #12158 | semidirect |
| 265. C2×C4 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031562 | 2 |
| #26022164 | 2 |
| #26018260 | 2 |
| #26018192 | 2 |
| C89×#2054 | 2 |
| #12158 | 89 |