Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22625445 | C2 | semidirect |
| 3. D73⋊#332 | C2 | semidirect |
| 5. #22624821 | C2 | semidirect |
| 6. #22624800 | C2 | semidirect |
| 217. C73 | #9167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626578 | 2 |
| #22625445 | 2 |
| D73⋊#332 | 2 |
| #22625227 | 2 |
| #22624821 | 2 |
| #22624800 | 2 |
| #22619743 | 2 |
| #9167 | 73 |