Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22610875 | C2 | semidirect |
| 4. #22608444 | C2 | semidirect |
| 5. #22607825 | C2 | semidirect |
| 6. #22607786 | C2 | semidirect |
| 11. #17988867 | C4 | semidirect |
| 12. #17988792 | C4 | semidirect |
| 31. #14556591 | C2×C4 | semidirect |
| 32. #14556591 | C2×C4 | semidirect |
| 46. C4⋊#10596831 | C2×C4 | semidirect |
| 193. C73 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620030 | 2 |
| #22612292 | 2 |
| #22610875 | 2 |
| #22608444 | 2 |
| #22607825 | 2 |
| #22607786 | 2 |
| C73×#1490 | 2 |
| #9323 | 73 |