Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 35. C4×#10596831 | C8 | semidirect |
| 36. C8×Dic73 | C8 | semidirect |
| 37. C8×Dic73 | C8 | semidirect |
| 38. C4×C8×C73 | C8 | semidirect |
| 116. C73 | #8780 | semidirect |
| 149. C4×C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22626941 | 2 |
| #22626934 | 2 |
| #22625587 | 2 |
| #8780 | 73 |