Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
994 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 166 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. #22625592 | C2 | semidirect |
| 2. #22624748 | C2 | semidirect |
| 3. #22624747 | C2 | semidirect |
| 7. #17989453 | C22 | semidirect |
| 27. C2×D4×D73 | C8 | semidirect |
| 60. C2×D292 | C2×C8 | semidirect |
| 92. C2×D4×C73 | C2×C8 | semidirect |
| 186. D73 | #1270 | semidirect |
| 191. C73 | C2×#1270 | semidirect |
| 253. C2×D4 | #11924036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625592 | 2 |
| #22624748 | 2 |
| #22624747 | 2 |
| #390×D73 | 2 |
| C2×#1270 | 73 |