Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
306 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 29. C4×#10596831 | C8 | semidirect |
| 30. C8×Dic73 | C8 | semidirect |
| 31. C8×Dic73 | C8 | semidirect |
| 32. C4×C8×C73 | C8 | semidirect |
| 102. C73 | #8800 | semidirect |
| 130. C4×C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626941 | 2 |
| #22626936 | 2 |
| #22626935 | 2 |
| C4×#14556645 | 2 |
| #8800 | 73 |