Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
300 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22611691 | C2 | semidirect |
| 5. #22608020 | C2 | semidirect |
| 6. #22608018 | C2 | semidirect |
| 7. C73×#2110 | C2 | semidirect |
| 141. #2110 | D73 | semidirect |
| 145. C73 | #13126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611691 | 2 |
| #22611558 | 2 |
| C2×#17988372 | 2 |
| #22609732 | 2 |
| #22608020 | 2 |
| #22608018 | 2 |
| C73×#2110 | 2 |
| #13126 | 73 |