Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2070 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 2070 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D73 |
| commutator, socle, cosocle | C23×C73 | C25 |
| Fitting | C73×#2840 | C2 |
| hypercenter | #2840 | D73 |
| hypocenter | C73 | #36675 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22618122 | C2 | semidirect |
| 2. #22618015 | C2 | semidirect |
| 3. #22617928 | C2 | semidirect |
| 4. #22613213 | C2 | semidirect |
| 5. #22613148 | C2 | semidirect |
| 6. #22612430 | C2 | semidirect |
| 7. C73×#2840 | C2 | semidirect |
| 8. C22×#11924029 | C22 | semidirect |
| 11. C2×Q8×Dic73 | C22 | semidirect |
| 13. #17988529 | C22 | semidirect |
| 14. #17988514 | C22 | semidirect |
| 16. #17988506 | C22 | semidirect |
| 17. #17988505 | C22 | semidirect |
| 19. #17988498 | C22 | semidirect |
| 24. #17988434 | C22 | semidirect |
| 25. #17988432 | C22 | semidirect |
| 76. C24×C73 | #41 | semidirect |
| 131. #2840 | D73 | semidirect |
| 138. C73 | #36675 | semidirect |
| 189. C24 | #11924029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618122 | 2 |
| #22618015 | 2 |
| #22617928 | 2 |
| #22613213 | 2 |
| #22613148 | 2 |
| #22612430 | 2 |
| C73×#2840 | 2 |
| #36675 | 73 |