Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
624 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 624 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 |
|---|---|---|
| 2. #22619000 | C2 | semidirect |
| 3. #22611594 | C2 | semidirect |
| 4. #22609895 | C2 | semidirect |
| 5. #22608060 | C2 | semidirect |
| 6. #22608059 | C2 | semidirect |
| 7. C73×#1794 | C2 | semidirect |
| 10. #17988770 | C4 | semidirect |
| 12. #17988760 | C4 | semidirect |
| 267. #1794 | D73 | semidirect |
| 270. C73 | #13053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619280 | 2 |
| #22619000 | 2 |
| #22611594 | 2 |
| #22609895 | 2 |
| #22608060 | 2 |
| #22608059 | 2 |
| C73×#1794 | 2 |
| #13053 | 73 |