Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
710 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22622563 | C2 | semidirect |
| 2. #22621596 | C2 | semidirect |
| 3. #22609393 | C2 | semidirect |
| 4. #22609372 | C2 | semidirect |
| 5. #22609177 | C2 | semidirect |
| 6. #22608993 | C2 | semidirect |
| 7. #22608817 | C2 | semidirect |
| 8. C8×Dic292 | C2 | semidirect |
| 9. C73×#1706 | C2 | semidirect |
| 95. Dic292 | D8 | semidirect |
| 184. #1706 | D73 | semidirect |
| 191. C73 | #19888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622563 | 2 |
| #22621596 | 2 |
| #22609393 | 2 |
| #22609372 | 2 |
| #22609177 | 2 |
| #22608993 | 2 |
| #22608817 | 2 |
| C8×Dic292 | 2 |
| C73×#1706 | 2 |
| #19888 | 73 |