Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22621540 | C2 | semidirect |
| 2. #22611963 | C2 | semidirect |
| 3. #22609407 | C2 | semidirect |
| 4. #22607974 | C2 | semidirect |
| 5. #22607899 | C2 | semidirect |
| 6. #22607890 | C2 | semidirect |
| 7. C73×#2250 | C2 | semidirect |
| 18. C4⋊#11924003 | C22 | semidirect |
| 20. #17988338 | C22 | semidirect |
| 25. #493×C73 | C22 | semidirect |
| 26. #346×C73 | C22 | semidirect |
| 80. D584 | D8 | semidirect |
| 181. #2250 | D73 | semidirect |
| 187. C73 | #12324 | semidirect |
| 194. #493 | C2×D73 | semidirect |
| 204. #346 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621540 | 2 |
| #22611963 | 2 |
| #22609407 | 2 |
| #22607974 | 2 |
| #22607899 | 2 |
| #22607890 | 2 |
| C73×#2250 | 2 |
| #12324 | 73 |