Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 3. #22609322 | C2 | semidirect |
| 4. #22607986 | C2 | semidirect |
| 5. #22607911 | C2 | semidirect |
| 7. C73×#2252 | C2 | semidirect |
| 61. D584 | Q16 | semidirect |
| 128. #2252 | D73 | semidirect |
| 134. C73 | #12404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622783 | 2 |
| #22612065 | 2 |
| #22609322 | 2 |
| #22607986 | 2 |
| #22607911 | 2 |
| #22607893 | 2 |
| C73×#2252 | 2 |
| #12404 | 73 |