Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
386 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 90 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. #22626287 | C2 | semidirect |
| 4. #22625009 | C2 | semidirect |
| 156. C73 | #12924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#430 | 2 |
| #22626287 | 2 |
| #22625812 | 2 |
| #22625009 | 2 |
| #349×D73 | 2 |
| #12924 | 73 |