Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
742 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22619189 | C2 | semidirect |
| 3. #22609842 | C2 | semidirect |
| 4. #22608295 | C2 | semidirect |
| 5. #22608291 | C2 | semidirect |
| 6. #22607808 | C2 | semidirect |
| 7. C73×#3187 | C2 | semidirect |
| 247. #3187 | D73 | semidirect |
| 254. C73 | #9975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619189 | 2 |
| #22619181 | 2 |
| #22609842 | 2 |
| #22608295 | 2 |
| #22608291 | 2 |
| #22607808 | 2 |
| C73×#3187 | 2 |
| #9975 | 73 |