Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
314 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. #22626289 | C2 | semidirect |
| 2. #22624870 | C2 | semidirect |
| 107. C73 | #11462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626289 | 2 |
| #22624870 | 2 |
| #22624853 | 2 |
| #22618571 | 2 |
| #11462 | 73 |