Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
500 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 204 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. #26012519 | C2 | semidirect |
| 2. #26012507 | C2 | semidirect |
| 3. D173⋊(C22⋊C8) | C2 | semidirect |
| 5. C2×D173⋊C8 | C22 | semidirect |
| 6. C4⋊#13063443 | C22 | semidirect |
| 7. #19149736 | C22 | semidirect |
| 9. C4×#13063443 | C22 | semidirect |
| 20. C2×D692 | C8 | semidirect |
| 36. C22×D173 | C2×C8 | semidirect |
| 38. D692 | C2×C8 | semidirect |
| 48. C2×C4×C173 | C2×C8 | semidirect |
| 69. C173 | #2972 | semidirect |
| 117. C2×C4 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012519 | 2 |
| #26012507 | 2 |
| D173⋊(C22⋊C8) | 2 |
| C2×#19149641 | 2 |
| #2972 | 173 |