Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018195 | C2 | semidirect |
| 4. #26018183 | C2 | semidirect |
| 5. C89×#1459 | C2 | semidirect |
| 29. #15668008 | C8 | semidirect |
| 62. C2×D356 | C2×C8 | semidirect |
| 86. C4×Dic89 | C2×C8 | semidirect |
| 207. #1459 | D89 | semidirect |
| 210. C89 | #11479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022974 | 2 |
| #26018570 | 2 |
| #26018195 | 2 |
| #26018183 | 2 |
| C89×#1459 | 2 |
| #11479 | 89 |