Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22610105 | C2 | semidirect |
| 2. #22608699 | C2 | semidirect |
| 5. #22607829 | C2 | semidirect |
| 6. #22607820 | C2 | semidirect |
| 176. C73 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610105 | 2 |
| #22608699 | 2 |
| #22608519 | 2 |
| #22608396 | 2 |
| #22607829 | 2 |
| #22607820 | 2 |
| C73×#2995 | 2 |
| #8916 | 73 |