Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
430 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 97 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×#17988404 | C2 | semidirect |
| 5. C2×#17988392 | C2 | semidirect |
| 6. #22610716 | C2 | semidirect |
| 7. C73×#1379 | C2 | semidirect |
| 187. #1379 | D73 | semidirect |
| 188. C73 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620425 | 2 |
| C2×#17988404 | 2 |
| C2×#17988395 | 2 |
| #22611644 | 2 |
| C2×#17988392 | 2 |
| #22610716 | 2 |
| C73×#1379 | 2 |
| #13412 | 73 |