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. #26012518 | C2 | semidirect |
| 2. #26012508 | C2 | semidirect |
| 3. D173⋊(C22⋊C8) | C2 | semidirect |
| 4. C2×C22⋊#13063443 | C2 | semidirect |
| 6. C2×D173⋊C8 | C22 | semidirect |
| 7. C22×#13063443 | C22 | semidirect |
| 8. #19149746 | C22 | semidirect |
| 9. #19149736 | C22 | semidirect |
| 11. C22⋊#13063443 | C22 | semidirect |
| 12. C4×#13063443 | C22 | semidirect |
| 26. C2×C22⋊D173 | C8 | semidirect |
| 48. C22×D173 | C2×C8 | semidirect |
| 50. C22⋊D173 | C2×C8 | semidirect |
| 55. C2×Dic173 | C2×C8 | semidirect |
| 64. C23×C173 | C2×C8 | semidirect |
| 95. C173 | #2972 | semidirect |
| 147. C23 | D173⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012518 | 2 |
| #26012508 | 2 |
| D173⋊(C22⋊C8) | 2 |
| C2×C22⋊#13063443 | 2 |
| C2×#19149639 | 2 |
| #2972 | 173 |