Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. #22624988 | C2 | semidirect |
| 13. C2×#14556525 | C4 | semidirect |
| 17. #107×D73 | C4 | semidirect |
| 19. C2×#107×C73 | C4 | semidirect |
| 149. C73 | #12867 | semidirect |
| 160. C2×#107 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626156 | 2 |
| #22625808 | 2 |
| #22624988 | 2 |
| C2×#107×D73 | 2 |
| #12867 | 73 |