Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22621543 | C2 | semidirect |
| 2. #22612197 | C2 | semidirect |
| 3. #22611967 | C2 | semidirect |
| 4. #22609410 | C2 | semidirect |
| 5. #22607975 | C2 | semidirect |
| 6. #22607899 | C2 | semidirect |
| 7. C73×#1330 | C2 | semidirect |
| 14. #17988964 | C22 | semidirect |
| 22. #17988338 | C22 | semidirect |
| 25. C4⋊C16×C73 | C22 | semidirect |
| 26. #346×C73 | C22 | semidirect |
| 92. D584 | D8 | semidirect |
| 186. #1330 | D73 | semidirect |
| 187. C73 | #12324 | semidirect |
| 202. C4⋊C16 | 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 |
|---|---|
| #22621543 | 2 |
| #22612197 | 2 |
| #22611967 | 2 |
| #22609410 | 2 |
| #22607975 | 2 |
| #22607899 | 2 |
| C73×#1330 | 2 |
| #12324 | 73 |