Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #26012201 | C2 | semidirect |
| 2. #26011855 | C2 | semidirect |
| 3. #26011837 | C2 | semidirect |
| 4. #26011791 | C2 | semidirect |
| 5. #26011781 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011683 | C2 | semidirect |
| 8. #26011622 | C2 | semidirect |
| 9. #26011601 | C2 | semidirect |
| 10. C4×#14583811 | C2 | semidirect |
| 11. #550×C173 | C2 | semidirect |
| 77. D692 | #41 | semidirect |
| 129. C173 | #3366 | semidirect |
| 132. #550 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012201 | 2 |
| #26011855 | 2 |
| #26011837 | 2 |
| #26011791 | 2 |
| #26011781 | 2 |
| #26011683 | 2 |
| #26011622 | 2 |
| #26011601 | 2 |
| C4×#14583811 | 2 |
| #550×C173 | 2 |
| #3366 | 173 |