Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
380 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #22607958 | C2 | semidirect |
| 5. #22607937 | C2 | semidirect |
| 6. #22607865 | C2 | semidirect |
| 7. C73×#2833 | C2 | semidirect |
| 177. #2833 | D73 | semidirect |
| 184. C73 | #12201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22610977 | 2 |
| #22608967 | 2 |
| #22608933 | 2 |
| #22607958 | 2 |
| #22607937 | 2 |
| #22607865 | 2 |
| C73×#2833 | 2 |
| #12201 | 73 |