Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
482 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#17988407 | C2 | semidirect |
| 3. C2×#17988403 | C2 | semidirect |
| 6. #22609812 | C2 | semidirect |
| 7. C73×#2141 | C2 | semidirect |
| 13. #17988972 | C4 | semidirect |
| 170. #2141 | D73 | semidirect |
| 173. C73 | #13260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988972 | 2 |
| C2×#17988407 | 2 |
| C2×#17988403 | 2 |
| C2×#17988401 | 2 |
| #22611646 | 2 |
| #22609812 | 2 |
| C73×#2141 | 2 |
| #13260 | 73 |