Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
414 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 42. C4×Dic73 | C16 | semidirect |
| 77. C4×C73 | C4⋊C16 | semidirect |
| 79. Dic73 | C4⋊C16 | semidirect |
| 92. C73 | #12898 | semidirect |
| 171. C4 | #17989690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989690 | 2 |
| C2×C4⋊#11924040 | 2 |
| C42×#10596833 | 2 |
| #12898 | 73 |