Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22620509 | C2 | semidirect |
| 2. #22620508 | C2 | semidirect |
| 3. #22620358 | C2 | semidirect |
| 4. #22620354 | C2 | semidirect |
| 5. #22609604 | C2 | semidirect |
| 6. #22609602 | C2 | semidirect |
| 7. #22609600 | C2 | semidirect |
| 8. #22609598 | C2 | semidirect |
| 9. #22609596 | C2 | semidirect |
| 10. #322×D73 | C2 | semidirect |
| 11. C73×#1721 | C2 | semidirect |
| 113. C8×D73 | D8 | semidirect |
| 202. #1721 | D73 | semidirect |
| 204. C73 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620509 | 2 |
| #22620508 | 2 |
| #22620358 | 2 |
| #22620354 | 2 |
| #22609604 | 2 |
| #22609602 | 2 |
| #22609600 | 2 |
| #22609598 | 2 |
| #22609596 | 2 |
| #322×D73 | 2 |
| C73×#1721 | 2 |
| #19616 | 73 |