Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 5. #19149754 | C4 | semidirect |
| 12. #19149615 | C4 | semidirect |
| 14. #108×C173 | C4 | semidirect |
| 60. C173 | #1387 | semidirect |
| 73. #108 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊M32 | 2 |
| C2×#19149748 | 2 |
| #108×D173 | 2 |
| #1387 | 173 |