Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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. #22620509 | C2 | semidirect |
| 2. #22620360 | C2 | semidirect |
| 3. #22620358 | C2 | semidirect |
| 4. #22609547 | C2 | semidirect |
| 5. #22609545 | C2 | semidirect |
| 6. #22609537 | C2 | semidirect |
| 7. #22609522 | C2 | semidirect |
| 8. C82×D73 | C2 | semidirect |
| 9. C73×#1709 | C2 | semidirect |
| 85. C8×D73 | D8 | semidirect |
| 124. #10596831 | #135 | semidirect |
| 150. #1709 | D73 | semidirect |
| 153. C73 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620509 | 2 |
| #22620360 | 2 |
| #22620358 | 2 |
| #22609547 | 2 |
| #22609545 | 2 |
| #22609537 | 2 |
| #22609522 | 2 |
| C82×D73 | 2 |
| C73×#1709 | 2 |
| #19603 | 73 |