Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. C2×#17988402 | C2 | semidirect |
| 5. #22610844 | C2 | semidirect |
| 6. #22608018 | C2 | semidirect |
| 7. C73×#1388 | C2 | semidirect |
| 12. #17989030 | C4 | semidirect |
| 172. #1388 | D73 | semidirect |
| 174. C73 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989030 | 2 |
| #22618847 | 2 |
| #22611678 | 2 |
| C2×#17988402 | 2 |
| #22610844 | 2 |
| #22608018 | 2 |
| C73×#1388 | 2 |
| #13031 | 73 |