Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
616 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018570 | C2 | semidirect |
| 3. #26018197 | C2 | semidirect |
| 4. #26018183 | C2 | semidirect |
| 5. C89×#1459 | C2 | semidirect |
| 29. #15668008 | C8 | semidirect |
| 64. C2×D356 | C2×C8 | semidirect |
| 92. C4×Dic89 | C2×C8 | semidirect |
| 214. #1459 | D89 | semidirect |
| 217. C89 | #11475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668008 | 2 |
| #26018570 | 2 |
| #26018197 | 2 |
| #26018183 | 2 |
| C89×#1459 | 2 |
| #11475 | 89 |