Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
984 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 274 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 |
|---|---|---|
| 1. #22625904 | C2 | semidirect |
| 2. #22625858 | C2 | semidirect |
| 23. #127×C73 | C8 | semidirect |
| 39. C2×D4×C73 | C2×C8 | semidirect |
| 41. C42×C73 | C2×C8 | semidirect |
| 75. C73 | #23355 | semidirect |
| 88. #127 | #10596833 | semidirect |
| 100. C2×D4 | C2×#10596833 | semidirect |
| 113. C42 | C2×#10596833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625904 | 2 |
| #22625858 | 2 |
| #127×Dic73 | 2 |
| #23355 | 73 |