Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
200 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 62. C4×C173 | #108 | semidirect |
| 72. C173 | #1950 | semidirect |
| 135. C4 | #19149614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149614 | 2 |
| #26011515 | 2 |
| C2×C4⋊#13063436 | 2 |
| #26011255 | 2 |
| C4×M16×C173 | 2 |
| #1950 | 173 |