Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. D73⋊#430 | C2 | semidirect |
| 2. #22626246 | C2 | semidirect |
| 3. #22626165 | C2 | semidirect |
| 4. #22625013 | C2 | semidirect |
| 36. #14556662 | D4 | semidirect |
| 202. C73 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#430 | 2 |
| #22626246 | 2 |
| #22626165 | 2 |
| #22625013 | 2 |
| #22619538 | 2 |
| #12998 | 73 |