Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
770 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #22610105 | C2 | semidirect |
| 4. #22610072 | C2 | semidirect |
| 6. #22609836 | C2 | semidirect |
| 7. C73×#1838 | C2 | semidirect |
| 112. #1838 | D73 | semidirect |
| 115. C73 | #20830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618563 | 2 |
| C2×#97×D73 | 2 |
| #22610105 | 2 |
| #22610072 | 2 |
| #22609968 | 2 |
| #22609836 | 2 |
| C73×#1838 | 2 |
| #20830 | 73 |