Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
598 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 24. C2×C42×C73 | C8 | semidirect |
| 113. C73 | #8699 | semidirect |
| 133. C2×C42 | #10596831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22609999 | 2 |
| #22607774 | 2 |
| C2×#376×C73 | 2 |
| #8699 | 73 |