Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22620649 | C2 | semidirect |
| 3. #22620325 | C2 | semidirect |
| 4. #22620312 | C2 | semidirect |
| 5. #22609584 | C2 | semidirect |
| 6. #22609577 | C2 | semidirect |
| 7. #22609570 | C2 | semidirect |
| 8. #22609543 | C2 | semidirect |
| 9. C73×#1455 | C2 | semidirect |
| 167. #1455 | D73 | semidirect |
| 168. C73 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620669 | 2 |
| #22620649 | 2 |
| #22620325 | 2 |
| #22620312 | 2 |
| #22609584 | 2 |
| #22609577 | 2 |
| #22609570 | 2 |
| #22609543 | 2 |
| C73×#1455 | 2 |
| #19754 | 73 |