Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 18. #19149671 | C4 | semidirect |
| 19. #19149670 | C4 | semidirect |
| 20. #19149669 | C4 | semidirect |
| 24. #125×C173 | C4 | semidirect |
| 91. C173 | #2330 | semidirect |
| 103. #125 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012442 | 2 |
| #26012440 | 2 |
| #26012437 | 2 |
| C4⋊C4×#10621924 | 2 |
| #26012427 | 2 |
| #125×D173 | 2 |
| #2330 | 173 |