Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
768 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 148 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. #22625020 | C2 | semidirect |
| 7. #17989566 | C4 | semidirect |
| 10. C2×#14556649 | C4 | semidirect |
| 12. C22×#11924012 | C4 | semidirect |
| 13. #17988555 | C4 | semidirect |
| 17. C22×M16×C73 | C4 | semidirect |
| 28. #14556649 | C2×C4 | semidirect |
| 44. C22×#10596831 | C2×C4 | semidirect |
| 50. C2×M16×C73 | C2×C4 | semidirect |
| 192. C73 | #12577 | semidirect |
| 195. C22×M16 | #64408 | semidirect |
| 225. C2×M16 | C2×#64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989566 | 2 |
| #22625020 | 2 |
| #22618375 | 2 |
| #12577 | 73 |