Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22618542 | C2 | semidirect |
| 3. #22612146 | C2 | semidirect |
| 4. #22611704 | C2 | semidirect |
| 5. C2×#17988401 | C2 | semidirect |
| 6. C73×#2115 | C2 | semidirect |
| 13. #17988636 | C22 | semidirect |
| 18. #17988410 | C22 | semidirect |
| 22. #349×C73 | C22 | semidirect |
| 136. #2115 | D73 | semidirect |
| 137. C73 | #33657 | semidirect |
| 153. #349 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619579 | 2 |
| #22618542 | 2 |
| #22612146 | 2 |
| #22611704 | 2 |
| C2×#17988401 | 2 |
| C73×#2115 | 2 |
| #33657 | 73 |