Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
378 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626287 | C2 | semidirect |
| 3. C2×#17989515 | C2 | semidirect |
| 5. #22625012 | C2 | semidirect |
| 6. #22624993 | C2 | semidirect |
| 25. #17988372 | C4 | semidirect |
| 26. #17988371 | C4 | semidirect |
| 27. #17988370 | C4 | semidirect |
| 28. #350×C73 | C4 | semidirect |
| 182. C73 | #12927 | semidirect |
| 202. #350 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626593 | 2 |
| #22626287 | 2 |
| C2×#17989515 | 2 |
| #22625818 | 2 |
| #22625012 | 2 |
| #22624993 | 2 |
| #350×D73 | 2 |
| #12927 | 73 |