Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22619070 | C2 | semidirect |
| 3. #22610858 | C2 | semidirect |
| 4. #22608644 | C2 | semidirect |
| 5. #22607800 | C2 | semidirect |
| 6. #22607787 | C2 | semidirect |
| 7. C73×#1509 | C2 | semidirect |
| 9. #17988977 | C4 | semidirect |
| 10. #17988953 | C4 | semidirect |
| 220. #1509 | D73 | semidirect |
| 223. C73 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620946 | 2 |
| #22619070 | 2 |
| #22610858 | 2 |
| #22608644 | 2 |
| #22607800 | 2 |
| #22607787 | 2 |
| C73×#1509 | 2 |
| #9378 | 73 |