Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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 |
|---|---|---|
| 2. #26012502 | C2 | semidirect |
| 3. #26012501 | C2 | semidirect |
| 4. C2×#19149747 | C2 | semidirect |
| 15. #19149687 | C4 | semidirect |
| 16. #19149686 | C4 | semidirect |
| 17. #19149685 | C4 | semidirect |
| 20. #131×C173 | C4 | semidirect |
| 33. #14583810 | C2×C4 | semidirect |
| 34. #14583809 | C2×C4 | semidirect |
| 35. C2×#13063436 | C2×C4 | semidirect |
| 36. C8×D173 | C2×C4 | semidirect |
| 37. C8×D173 | C2×C4 | semidirect |
| 41. M16×C173 | C2×C4 | semidirect |
| 42. C2×C8×C173 | C2×C4 | semidirect |
| 76. C173 | #2912 | semidirect |
| 87. #131 | #10621924 | semidirect |
| 108. M16 | C2×#10621924 | semidirect |
| 114. C2×C8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012560 | 2 |
| #26012502 | 2 |
| #26012501 | 2 |
| C2×#19149747 | 2 |
| #131×D173 | 2 |
| #2912 | 173 |