Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 173 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. C4×#10596831 | C8 | semidirect |
| 27. C8×Dic73 | C8 | semidirect |
| 28. C4×C8×C73 | C8 | semidirect |
| 72. C8×C73 | C4⋊C8 | semidirect |
| 73. #10596831 | C4⋊C8 | semidirect |
| 84. C4×C73 | #335 | semidirect |
| 86. Dic73 | #335 | semidirect |
| 97. C73 | #8806 | semidirect |
| 122. C4×C8 | #10596842 | semidirect |
| 167. C8 | C4⋊#10596842 | semidirect |
| 180. C4 | #17989677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627075 | 2 |
| C2×#17989677 | 2 |
| C4×C8×#64408 | 2 |
| #8806 | 73 |