Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
412 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 146 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. #26012524 | C2 | semidirect |
| 2. #26012523 | C2 | semidirect |
| 3. #26012521 | C2 | semidirect |
| 4. #26012519 | C2 | semidirect |
| 5. #26012516 | C2 | semidirect |
| 6. #26012466 | C2 | semidirect |
| 7. #26012463 | C2 | semidirect |
| 8. D173⋊(C22⋊C8) | C2 | semidirect |
| 10. C2×#14583836 | C22 | semidirect |
| 15. C2×D173⋊C8 | C22 | semidirect |
| 16. #19149746 | C22 | semidirect |
| 17. C4⋊#13063443 | C22 | semidirect |
| 21. #19149736 | C22 | semidirect |
| 22. #19149736 | C22 | semidirect |
| 24. #19149734 | C22 | semidirect |
| 25. C4×#13063443 | C22 | semidirect |
| 137. C173 | #2976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012524 | 2 |
| #26012523 | 2 |
| #26012521 | 2 |
| #26012519 | 2 |
| #26012516 | 2 |
| #26012466 | 2 |
| #26012463 | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012004 | 2 |
| #2976 | 173 |