Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
936 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. #22621121 | C2 | semidirect |
| 3. #22609242 | C2 | semidirect |
| 4. #22609229 | C2 | semidirect |
| 5. #22608555 | C2 | semidirect |
| 6. #22608533 | C2 | semidirect |
| 7. C2×#563×C73 | C2 | semidirect |
| 11. #17988997 | C22 | semidirect |
| 15. #17988953 | C22 | semidirect |
| 21. #17988329 | C22 | semidirect |
| 187. C2×#563 | D73 | semidirect |
| 194. C73 | #18994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621121 | 2 |
| #22620395 | 2 |
| #22609242 | 2 |
| #22609229 | 2 |
| #22608555 | 2 |
| #22608533 | 2 |
| C2×#563×C73 | 2 |
| #18994 | 73 |