Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C2×#17988324 | C2 | semidirect |
| 5. #22607818 | C2 | semidirect |
| 6. #22607773 | C2 | semidirect |
| 7. C73×#1472 | C2 | semidirect |
| 10. #17988917 | C4 | semidirect |
| 11. #17988900 | C4 | semidirect |
| 15. #17988743 | C4 | semidirect |
| 16. #17988726 | C4 | semidirect |
| 238. #1472 | D73 | semidirect |
| 241. C73 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620712 | 2 |
| #22618985 | 2 |
| #22608436 | 2 |
| C2×#17988324 | 2 |
| #22607818 | 2 |
| #22607773 | 2 |
| C73×#1472 | 2 |
| #9263 | 73 |