Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 3. #22611425 | C2 | semidirect |
| 4. #22607943 | C2 | semidirect |
| 6. #22607870 | C2 | semidirect |
| 7. C73×#2236 | C2 | semidirect |
| 154. #2236 | D73 | semidirect |
| 160. C73 | #12293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621284 | 2 |
| #22612116 | 2 |
| #22611425 | 2 |
| #22607943 | 2 |
| #22607941 | 2 |
| #22607870 | 2 |
| C73×#2236 | 2 |
| #12293 | 73 |