Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
344 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22611623 | C2 | semidirect |
| 3. #22608105 | C2 | semidirect |
| 4. #22608087 | C2 | semidirect |
| 5. C73×#2127 | C2 | semidirect |
| 6. #17989192 | C4 | semidirect |
| 8. #17988963 | C4 | semidirect |
| 9. #17988951 | C4 | semidirect |
| 15. #17988648 | C4 | semidirect |
| 28. #14556588 | C2×C4 | semidirect |
| 29. #14556583 | C2×C4 | semidirect |
| 42. #14556502 | C2×C4 | semidirect |
| 43. C4×#10596831 | C2×C4 | semidirect |
| 161. #2127 | D73 | semidirect |
| 164. C73 | #13605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620981 | 2 |
| #22611623 | 2 |
| #22608105 | 2 |
| #22608087 | 2 |
| C73×#2127 | 2 |
| #13605 | 73 |