Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
262 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 16. #17988416 | C4 | semidirect |
| 116. C73 | #13173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988416 | 2 |
| #22611530 | 2 |
| #22610722 | 2 |
| #22610719 | 2 |
| #22608043 | 2 |
| C73×#1388 | 2 |
| #13173 | 73 |