Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #26012097 | C2 | direct (N × H) |
| 2. C2×#19149676 | C2 | semidirect |
| 3. C2×#19149664 | C2 | semidirect |
| 4. C2×#19149654 | C2 | semidirect |
| 5. C2×#19149654 | C2 | semidirect |
| 6. C2×#19149641 | C2 | semidirect |
| 7. C2×#19149636 | C2 | semidirect |
| 8. C2×#125×C173 | C2 | semidirect |
| 14. #19149676 | C22 | semidirect |
| 15. #19149664 | C22 | semidirect |
| 16. #19149654 | C22 | semidirect |
| 17. #19149654 | C22 | semidirect |
| 18. #19149641 | C22 | semidirect |
| 19. #19149636 | C22 | semidirect |
| 25. #125×C173 | C22 | semidirect |
| 92. C2×C173 | #540 | semidirect |
| 97. C173 | C2×#540 | semidirect |
| 101. C2×#125 | D173 | semidirect |
| 113. #125 | C2×D173 | semidirect |
| 192. C2 | #26012097 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012097 | 2 |
| C2×#19149676 | 2 |
| C2×#19149664 | 2 |
| C2×#19149654 | 2 |
| C2×#19149641 | 2 |
| C2×#19149636 | 2 |
| C2×#125×C173 | 2 |
| C2×#540 | 173 |