Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
684 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4×C4⋊#10596842 | C2 | semidirect |
| 2. #22626930 | C2 | semidirect |
| 31. #14556588 | C8 | semidirect |
| 33. #14556587 | C8 | semidirect |
| 35. #127×C73 | C8 | semidirect |
| 136. C73 | #7569 | semidirect |
| 154. #127 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#10596842 | 2 |
| #22626930 | 2 |
| #127×#64408 | 2 |
| #7569 | 73 |