Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22610921 | C2 | semidirect |
| 4. #22608526 | C2 | semidirect |
| 6. #22607822 | C2 | semidirect |
| 7. C73×#3229 | C2 | semidirect |
| 178. #3229 | D73 | semidirect |
| 184. C73 | #10111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621314 | 2 |
| #22620327 | 2 |
| #22610921 | 2 |
| #22608526 | 2 |
| #22608347 | 2 |
| #22607822 | 2 |
| C73×#3229 | 2 |
| #10111 | 73 |