Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
364 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22607920 | C2 | semidirect |
| 5. #22607919 | C2 | semidirect |
| 6. #22607918 | C2 | semidirect |
| 7. C73×#1340 | C2 | semidirect |
| 8. C2×Q16×D73 | C4 | semidirect |
| 12. #17988846 | C4 | semidirect |
| 14. #17988842 | C4 | semidirect |
| 18. #17988622 | C4 | semidirect |
| 184. #1340 | D73 | semidirect |
| 185. C73 | #11869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619584 | 2 |
| #22611550 | 2 |
| #22609976 | 2 |
| #22607920 | 2 |
| #22607919 | 2 |
| #22607918 | 2 |
| C73×#1340 | 2 |
| #11869 | 73 |