Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
362 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22612013 | C2 | semidirect |
| 3. #22612012 | C2 | semidirect |
| 4. #22609602 | C2 | semidirect |
| 5. #22607971 | C2 | semidirect |
| 6. #22607908 | C2 | semidirect |
| 7. C73×#1336 | C2 | semidirect |
| 13. #17988967 | C22 | semidirect |
| 21. #17988408 | C22 | semidirect |
| 25. #364×C73 | C22 | semidirect |
| 26. #322×C73 | C22 | semidirect |
| 181. #1336 | D73 | semidirect |
| 182. C73 | #12315 | semidirect |
| 198. #364 | C2×D73 | semidirect |
| 201. #322 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621725 | 2 |
| #22612013 | 2 |
| #22612012 | 2 |
| #22609602 | 2 |
| #22607971 | 2 |
| #22607908 | 2 |
| C73×#1336 | 2 |
| #12315 | 73 |