Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 3. #22608101 | C2 | semidirect |
| 4. #22608095 | C2 | semidirect |
| 6. #17989199 | C4 | semidirect |
| 7. #17988982 | C4 | semidirect |
| 10. #17988941 | C4 | semidirect |
| 15. #17988648 | C4 | semidirect |
| 27. #14556591 | C2×C4 | semidirect |
| 29. #14556583 | C2×C4 | semidirect |
| 42. #14556502 | C2×C4 | semidirect |
| 43. C4×#10596831 | C2×C4 | semidirect |
| 159. C73 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621003 | 2 |
| #22611600 | 2 |
| #22608101 | 2 |
| #22608095 | 2 |
| C73×#2128 | 2 |
| #13610 | 73 |