Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22621314 | C2 | semidirect |
| 3. #22610909 | C2 | semidirect |
| 4. #22610760 | C2 | semidirect |
| 5. #22610758 | C2 | semidirect |
| 6. #22607844 | C2 | semidirect |
| 7. C73×#3254 | C2 | semidirect |
| 220. #3254 | D73 | semidirect |
| 226. C73 | #10301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621314 | 2 |
| #22621309 | 2 |
| #22610909 | 2 |
| #22610760 | 2 |
| #22610758 | 2 |
| #22607844 | 2 |
| C73×#3254 | 2 |
| #10301 | 73 |