Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
646 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #22618393 | C2 | semidirect |
| 3. #22611602 | C2 | semidirect |
| 4. #22611582 | C2 | semidirect |
| 5. #22609907 | C2 | semidirect |
| 6. #22608052 | C2 | semidirect |
| 7. C73×#1395 | C2 | semidirect |
| 9. C2×#14556619 | C4 | semidirect |
| 10. C22×#11924017 | C4 | semidirect |
| 19. #17988597 | C4 | semidirect |
| 20. #17988584 | C4 | semidirect |
| 253. #1395 | D73 | semidirect |
| 255. C73 | #13103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619219 | 2 |
| #22618393 | 2 |
| #22611602 | 2 |
| #22611582 | 2 |
| #22609907 | 2 |
| #22608052 | 2 |
| C73×#1395 | 2 |
| #13103 | 73 |