Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22618985 | C2 | semidirect |
| 3. #22608436 | C2 | semidirect |
| 4. C2×#17988321 | C2 | semidirect |
| 5. #22607818 | C2 | semidirect |
| 6. #22607773 | C2 | semidirect |
| 7. C73×#1471 | C2 | semidirect |
| 9. #17988922 | C4 | semidirect |
| 11. #17988905 | C4 | semidirect |
| 14. #17988738 | C4 | semidirect |
| 16. #17988721 | C4 | semidirect |
| 250. #1471 | D73 | semidirect |
| 253. C73 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620696 | 2 |
| #22618985 | 2 |
| #22608436 | 2 |
| C2×#17988321 | 2 |
| #22607818 | 2 |
| #22607773 | 2 |
| C73×#1471 | 2 |
| #9264 | 73 |