Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
346 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 346 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. #22607914 | C2 | semidirect |
| 5. #22607913 | C2 | semidirect |
| 6. #22607912 | C2 | semidirect |
| 7. C73×#1338 | C2 | semidirect |
| 146. D73 | #1338 | direct (N × H) |
| 153. #1338 | D73 | direct (N × H) |
| 154. C73 | C2×#1338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #446×D73 | 2 |
| C4⋊C16×D73 | 2 |
| #346×D73 | 2 |
| #22607914 | 2 |
| #22607913 | 2 |
| #22607912 | 2 |
| C73×#1338 | 2 |
| C2×#1338 | 73 |