Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012042 | C2 | semidirect |
| 2. #26011868 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011728 | C2 | semidirect |
| 5. #26011573 | C2 | semidirect |
| 6. C4×C8×D173 | C2 | semidirect |
| 7. #500×C173 | C2 | semidirect |
| 58. C4×D173 | D8 | semidirect |
| 65. C8×C173 | #41 | semidirect |
| 85. C173 | #3169 | semidirect |
| 88. #500 | D173 | semidirect |
| 151. C8 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012042 | 2 |
| #26011868 | 2 |
| #26011839 | 2 |
| #26011728 | 2 |
| #26011573 | 2 |
| C4×C8×D173 | 2 |
| #500×C173 | 2 |
| #3169 | 173 |