Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×#14556510 | C2 | semidirect |
| 3. #22607959 | C2 | semidirect |
| 5. C73×#1461 | C2 | semidirect |
| 171. #1461 | D73 | semidirect |
| 174. C73 | #11734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22613214 | 2 |
| C4×#14556510 | 2 |
| #22607959 | 2 |
| #22607935 | 2 |
| C73×#1461 | 2 |
| #11734 | 73 |