Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
616 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 616 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. #26018570 | C2 | semidirect |
| 2. #26018198 | C2 | semidirect |
| 3. #26018184 | C2 | semidirect |
| 26. #127×C89 | C8 | semidirect |
| 57. C2×D4×C89 | C2×C8 | semidirect |
| 85. C42×C89 | C2×C8 | semidirect |
| 162. C89 | #11475 | semidirect |
| 182. #127 | #10623494 | semidirect |
| 213. C2×D4 | C2×#10623494 | semidirect |
| 243. C42 | C2×#10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018570 | 2 |
| #26018198 | 2 |
| #26018184 | 2 |
| C4×#127×C89 | 2 |
| #11475 | 89 |