Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 4. C2×#14556666 | C4 | semidirect |
| 5. C2×#14556664 | C4 | semidirect |
| 10. #17989455 | C4 | semidirect |
| 14. #17988344 | C4 | semidirect |
| 15. H(3,ℤ/4)×C73 | C4 | semidirect |
| 122. C73 | #7228 | semidirect |
| 134. H(3,ℤ/4) | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626162 | 2 |
| #22625814 | 2 |
| #22609976 | 2 |
| #7228 | 73 |