Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22611558 | C2 | semidirect |
| 3. C2×#17988372 | C2 | semidirect |
| 4. #22611545 | C2 | semidirect |
| 5. C73×#2115 | C2 | semidirect |
| 14. C2×#14556531 | C22 | semidirect |
| 15. C22×#11924003 | C22 | semidirect |
| 20. C2×M32×C73 | C22 | semidirect |
| 168. #2115 | D73 | semidirect |
| 170. C73 | #12685 | semidirect |
| 181. C2×M32 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624642 | 2 |
| #22611558 | 2 |
| C2×#17988372 | 2 |
| #22611545 | 2 |
| C73×#2115 | 2 |
| #12685 | 73 |