Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #22610751 | C2 | semidirect |
| 4. #22608602 | C2 | semidirect |
| 6. #22607790 | C2 | semidirect |
| 7. C73×#1275 | C2 | semidirect |
| 11. #17988992 | C4 | semidirect |
| 12. #17988934 | C4 | semidirect |
| 188. #1275 | D73 | semidirect |
| 189. C73 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621054 | 2 |
| #22618650 | 2 |
| #22610751 | 2 |
| #22608602 | 2 |
| #22608492 | 2 |
| #22607790 | 2 |
| C73×#1275 | 2 |
| #9291 | 73 |