Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22617914 | C2 | semidirect |
| 5. #22607957 | C2 | semidirect |
| 6. #22607864 | C2 | semidirect |
| 7. C73×#1353 | C2 | semidirect |
| 184. #1353 | D73 | semidirect |
| 186. C73 | #12131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22617914 | 2 |
| #22610980 | 2 |
| #22608970 | 2 |
| #22608967 | 2 |
| #22607957 | 2 |
| #22607864 | 2 |
| C73×#1353 | 2 |
| #12131 | 73 |