Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
274 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 2. #22612214 | C2 | semidirect |
| 4. #22607982 | C2 | semidirect |
| 5. #22607901 | C2 | semidirect |
| 7. C73×#2225 | C2 | semidirect |
| 137. #2225 | D73 | semidirect |
| 142. C73 | #12401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22622507 | 2 |
| #22612214 | 2 |
| #22609451 | 2 |
| #22607982 | 2 |
| #22607901 | 2 |
| #22607888 | 2 |
| C73×#2225 | 2 |
| #12401 | 73 |