Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
262 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 6. #17989682 | C4 | semidirect |
| 8. #17989677 | C4 | semidirect |
| 26. #14556659 | C8 | semidirect |
| 34. #14556523 | C8 | semidirect |
| 36. #106×C73 | C8 | semidirect |
| 116. C73 | #7175 | semidirect |
| 141. #106 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64408⋊M32 | 2 |
| #22627055 | 2 |
| #106×#64408 | 2 |
| #7175 | 73 |