Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
770 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 175 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. #22620677 | C2 | semidirect |
| 3. #22620472 | C2 | semidirect |
| 5. #22609605 | C2 | semidirect |
| 6. #22609600 | C2 | semidirect |
| 7. #22609565 | C2 | semidirect |
| 8. #22609550 | C2 | semidirect |
| 9. #22609549 | C2 | semidirect |
| 10. #22608233 | C2 | semidirect |
| 11. C73×#1705 | C2 | semidirect |
| 156. C8×C73 | #137 | semidirect |
| 187. #1705 | D73 | semidirect |
| 189. C73 | #19746 | semidirect |
| 336. C8 | #14556620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620677 | 2 |
| #22620647 | 2 |
| #22620472 | 2 |
| #22620385 | 2 |
| #22609605 | 2 |
| #22609600 | 2 |
| #22609565 | 2 |
| #22609550 | 2 |
| #22609549 | 2 |
| #22608233 | 2 |
| C73×#1705 | 2 |
| #19746 | 73 |