Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
516 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
|---|---|---|
| 127. C4×C73 | #333 | semidirect |
| 145. C73 | #8587 | semidirect |
| 275. C4 | #17989447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625864 | 2 |
| C2×#17989447 | 2 |
| #22624809 | 2 |
| C4×#14556589 | 2 |
| #8587 | 73 |