Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #17989512 | C4 | semidirect |
| 15. #17989511 | C4 | semidirect |
| 16. #17989474 | C4 | semidirect |
| 17. C16×#64408 | C4 | semidirect |
| 23. #17988411 | C4 | semidirect |
| 24. #17988410 | C4 | semidirect |
| 25. #17988409 | C4 | semidirect |
| 26. #365×C73 | C4 | semidirect |
| 146. C73 | #12668 | semidirect |
| 161. #365 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626279 | 2 |
| M32×#64408 | 2 |
| #22625736 | 2 |
| #22625734 | 2 |
| #22625000 | 2 |
| #22624998 | 2 |
| #22611702 | 2 |
| #12668 | 73 |