Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
756 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26018573 | C2 | semidirect |
| 2. #26018570 | C2 | semidirect |
| 3. #26018200 | C2 | semidirect |
| 4. #26018180 | C2 | semidirect |
| 41. #120×C89 | C8 | semidirect |
| 70. C24×C89 | C2×C8 | semidirect |
| 116. C22⋊C4×C89 | C2×C8 | semidirect |
| 235. C89 | #11471 | semidirect |
| 266. #120 | #10623494 | semidirect |
| 297. C24 | C2×#10623494 | semidirect |
| 346. C22⋊C4 | C2×#10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018573 | 2 |
| #26018570 | 2 |
| #26018200 | 2 |
| #26018180 | 2 |
| C4×#120×C89 | 2 |
| #11471 | 89 |