Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 11. #19149590 | C4 | semidirect |
| 12. #19149589 | C4 | semidirect |
| 13. #97×C173 | C4 | semidirect |
| 60. C173 | #1836 | semidirect |
| 73. #97 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012437 | 2 |
| #26012435 | 2 |
| #26012365 | 2 |
| #97×D173 | 2 |
| #1836 | 173 |