Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 4. #22610151 | C2 | semidirect |
| 5. #22608061 | C2 | semidirect |
| 6. #22608060 | C2 | semidirect |
| 7. C73×#1858 | C2 | semidirect |
| 20. #17988385 | C4 | semidirect |
| 21. #17988383 | C4 | semidirect |
| 192. #1858 | D73 | semidirect |
| 195. C73 | #12975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618995 | 2 |
| #22611614 | 2 |
| #22610314 | 2 |
| #22610151 | 2 |
| #22608061 | 2 |
| #22608060 | 2 |
| C73×#1858 | 2 |
| #12975 | 73 |