Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C2×#17988364 | C2 | semidirect |
| 5. #22609817 | C2 | semidirect |
| 6. #22608029 | C2 | semidirect |
| 7. C73×#1386 | C2 | semidirect |
| 12. #17988698 | C4 | semidirect |
| 17. #17988401 | C4 | semidirect |
| 18. #17988387 | C4 | semidirect |
| 40. C2×#11924003 | C2×C4 | semidirect |
| 42. #14556527 | C2×C4 | semidirect |
| 52. M32×C73 | C2×C4 | semidirect |
| 54. #107×C73 | C2×C4 | semidirect |
| 151. #1386 | D73 | semidirect |
| 153. C73 | #12647 | semidirect |
| 190. M32 | C4×D73 | semidirect |
| 195. #107 | C4×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988698 | 2 |
| C2×#17988401 | 2 |
| #22611646 | 2 |
| C2×#17988364 | 2 |
| #22609817 | 2 |
| #22608029 | 2 |
| C73×#1386 | 2 |
| #12647 | 73 |