Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 17. #17988404 | C4 | semidirect |
| 139. C73 | #12954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618798 | 2 |
| C2×#17988404 | 2 |
| C2×#17988402 | 2 |
| #22610719 | 2 |
| #22608047 | 2 |
| #22608018 | 2 |
| C73×#2155 | 2 |
| #12954 | 73 |