Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
774 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22627075 | C2 | semidirect |
| 2. C42×#10596842 | C2 | semidirect |
| 3. C2×D4⋊#10596842 | C2 | semidirect |
| 23. C4×#10596842 | D4 | semidirect |
| 39. #14556588 | C8 | semidirect |
| 41. #14556587 | C8 | semidirect |
| 43. #127×C73 | C8 | semidirect |
| 137. C4×C73 | D4⋊C8 | semidirect |
| 139. Dic73 | D4⋊C8 | semidirect |
| 153. C73 | #9638 | semidirect |
| 174. #127 | #10596842 | semidirect |
| 288. C4 | D4⋊#10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627075 | 2 |
| C42×#10596842 | 2 |
| C2×D4⋊#10596842 | 2 |
| #127×#64408 | 2 |
| #9638 | 73 |