Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22611696 | C2 | semidirect |
| 4. #22611528 | C2 | semidirect |
| 6. #22608021 | C2 | semidirect |
| 7. C73×#1378 | C2 | semidirect |
| 148. #1378 | D73 | semidirect |
| 149. C73 | #13123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611696 | 2 |
| #22611558 | 2 |
| C2×#17988372 | 2 |
| #22611528 | 2 |
| #22609732 | 2 |
| #22608021 | 2 |
| C73×#1378 | 2 |
| #13123 | 73 |