Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 1. #22621061 | C2 | semidirect |
| 2. #22620889 | C2 | semidirect |
| 4. #22620312 | C2 | semidirect |
| 5. #22609591 | C2 | semidirect |
| 6. #22609570 | C2 | semidirect |
| 7. #22609564 | C2 | semidirect |
| 8. #22609532 | C2 | semidirect |
| 9. C73×#1453 | C2 | semidirect |
| 167. #1453 | D73 | semidirect |
| 168. C73 | #19724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621061 | 2 |
| #22620889 | 2 |
| #22620669 | 2 |
| #22620312 | 2 |
| #22609591 | 2 |
| #22609570 | 2 |
| #22609564 | 2 |
| #22609532 | 2 |
| C73×#1453 | 2 |
| #19724 | 73 |