Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1334 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 400 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 |
|---|---|---|
| 3. C2×#17989446 | C2 | direct (N × H) |
| 11. #17989446 | C22 | direct (N × H) |
| 116. C22×C73 | #332 | semidirect |
| 132. C2×C73 | C2×#332 | semidirect |
| 140. C73 | C22×#332 | semidirect |
| 252. C22 | #17989446 | direct (N × H) |
| 267. C2 | C2×#17989446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556658 | 2 |
| C2×#17989446 | 2 |
| C22×#14556590 | 2 |
| C22×#332 | 73 |