Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #22607981 | C2 | semidirect |
| 5. #22607980 | C2 | semidirect |
| 6. #22607979 | C2 | semidirect |
| 7. C73×#1362 | C2 | semidirect |
| 140. D73 | #1362 | direct (N × H) |
| 147. #1362 | D73 | direct (N × H) |
| 148. C73 | C2×#1362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #494×D73 | 2 |
| C4⋊C16×D73 | 2 |
| #335×D73 | 2 |
| #22607981 | 2 |
| #22607980 | 2 |
| #22607979 | 2 |
| C73×#1362 | 2 |
| C2×#1362 | 73 |