Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 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 |
|---|---|---|
| 2. #22613111 | C2 | semidirect |
| 3. #22608656 | C2 | semidirect |
| 6. #22607796 | C2 | semidirect |
| 7. C73×#1288 | C2 | semidirect |
| 12. #17988967 | C4 | semidirect |
| 13. #17988960 | C4 | semidirect |
| 163. #1288 | D73 | semidirect |
| 164. C73 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620390 | 2 |
| #22613111 | 2 |
| #22608656 | 2 |
| #22608479 | 2 |
| #22608477 | 2 |
| #22607796 | 2 |
| C73×#1288 | 2 |
| #9429 | 73 |