Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
930 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22620689 | C2 | semidirect |
| 3. #22613578 | C2 | semidirect |
| 4. #22610766 | C2 | semidirect |
| 5. #22608502 | C2 | semidirect |
| 6. #22607778 | C2 | semidirect |
| 7. C73×#1786 | C2 | semidirect |
| 257. #1786 | D73 | semidirect |
| 260. C73 | #9947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620689 | 2 |
| C2×#17988721 | 2 |
| #22613578 | 2 |
| #22610766 | 2 |
| #22608502 | 2 |
| #22607778 | 2 |
| C73×#1786 | 2 |
| #9947 | 73 |