Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 26. #14556525 | C8 | semidirect |
| 28. #107×C73 | C8 | semidirect |
| 108. C73 | #7121 | semidirect |
| 129. #107 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627002 | 2 |
| #22626937 | 2 |
| #22626035 | 2 |
| #7121 | 73 |