Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #26012571 | C2 | semidirect |
| 2. #26012537 | C2 | semidirect |
| 3. #26012535 | C2 | semidirect |
| 4. D173⋊#108 | C2 | semidirect |
| 5. #26012490 | C2 | semidirect |
| 6. #26012454 | C2 | semidirect |
| 9. #19149767 | C22 | semidirect |
| 14. #19149750 | C22 | semidirect |
| 15. #19149749 | C22 | semidirect |
| 16. #19149744 | C22 | semidirect |
| 17. #19149733 | C22 | semidirect |
| 18. C8×#10621924 | C22 | semidirect |
| 20. #19149702 | C4 | semidirect |
| 21. #19149702 | C4 | semidirect |
| 24. C2×#14583813 | C4 | semidirect |
| 25. C2×D1384 | C4 | semidirect |
| 27. C2×Q16×C173 | C4 | semidirect |
| 101. C173 | #2957 | semidirect |
| 115. C2×Q16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012571 | 2 |
| #26012537 | 2 |
| #26012535 | 2 |
| D173⋊#108 | 2 |
| #26012490 | 2 |
| #26012454 | 2 |
| C2×#19149702 | 2 |
| #2957 | 173 |