Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
446 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22627117 | C2 | semidirect |
| 2. C2×#17989687 | C2 | semidirect |
| 3. C4×#14556688 | C2 | semidirect |
| 22. #14556688 | D4 | semidirect |
| 117. C4×C73 | #350 | semidirect |
| 134. C73 | #13193 | semidirect |
| 252. C4 | #17989687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627117 | 2 |
| C2×#17989687 | 2 |
| C4×#14556688 | 2 |
| #22626653 | 2 |
| #13193 | 73 |