Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
392 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 2. #22611550 | C2 | semidirect |
| 3. #22609980 | C2 | semidirect |
| 4. #22607923 | C2 | semidirect |
| 5. #22607922 | C2 | semidirect |
| 6. #22607921 | C2 | semidirect |
| 7. C73×#1341 | C2 | semidirect |
| 21. #17988369 | C22 | semidirect |
| 23. #17988345 | C22 | semidirect |
| 25. #349×C73 | C22 | semidirect |
| 26. #338×C73 | C22 | semidirect |
| 195. #1341 | D73 | semidirect |
| 196. C73 | #11870 | semidirect |
| 213. #349 | C2×D73 | semidirect |
| 215. #338 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619577 | 2 |
| #22611550 | 2 |
| #22609980 | 2 |
| #22607923 | 2 |
| #22607922 | 2 |
| #22607921 | 2 |
| C73×#1341 | 2 |
| #11870 | 73 |