Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22620669 | C2 | semidirect |
| 2. #22612145 | C2 | semidirect |
| 3. #22612102 | C2 | semidirect |
| 4. #22612007 | C2 | semidirect |
| 5. #22611877 | C2 | semidirect |
| 6. #22611829 | C2 | semidirect |
| 7. #22611743 | C2 | semidirect |
| 8. C73×#2956 | C2 | semidirect |
| 11. #17988985 | C22 | semidirect |
| 12. #17988964 | C22 | semidirect |
| 17. #17988700 | C22 | semidirect |
| 18. #17988411 | C22 | semidirect |
| 19. #17988408 | C22 | semidirect |
| 20. #17988399 | C22 | semidirect |
| 23. #17988365 | C22 | semidirect |
| 96. Q16×C73 | #41 | semidirect |
| 100. D8×C73 | #41 | semidirect |
| 171. #2956 | D73 | semidirect |
| 178. C73 | #33688 | semidirect |
| 259. Q16 | #11924028 | semidirect |
| 265. D8 | #11924028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620669 | 2 |
| #22612145 | 2 |
| #22612102 | 2 |
| #22612007 | 2 |
| #22611877 | 2 |
| #22611829 | 2 |
| #22611743 | 2 |
| C73×#2956 | 2 |
| #33688 | 73 |