Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 9. #19149748 | C4 | semidirect |
| 10. #19149747 | C4 | semidirect |
| 15. #19149590 | C4 | semidirect |
| 16. #19149589 | C4 | semidirect |
| 17. #19149589 | C4 | semidirect |
| 18. #97×C173 | C4 | semidirect |
| 55. #13063436 | C42 | semidirect |
| 59. C8×C173 | C42 | semidirect |
| 78. C173 | #1776 | semidirect |
| 96. #97 | #10621924 | semidirect |
| 138. C8 | C4×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149748 | 2 |
| C2×#19149747 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012365 | 2 |
| #97×D173 | 2 |
| #1776 | 173 |