Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1236 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 231 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. #22618411 | C2 | semidirect |
| 3. #22610480 | C2 | semidirect |
| 4. #22610346 | C2 | semidirect |
| 5. #22610043 | C2 | semidirect |
| 6. #22609855 | C2 | semidirect |
| 7. C73×#1784 | C2 | semidirect |
| 195. #1784 | D73 | semidirect |
| 196. C73 | #21780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623582 | 2 |
| #22618411 | 2 |
| #22610480 | 2 |
| #22610346 | 2 |
| #22610043 | 2 |
| #22609855 | 2 |
| C73×#1784 | 2 |
| #21780 | 73 |