Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
510 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 510 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. C22×#14556687 | C2 | semidirect |
| 2. C2×#17989685 | C2 | semidirect |
| 3. #22627098 | C2 | semidirect |
| 4. #22627007 | C2 | semidirect |
| 29. #14556687 | D4 | semidirect |
| 169. C22×C73 | #349 | semidirect |
| 193. C73 | #12985 | semidirect |
| 357. C22 | #17989685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556687 | 2 |
| C2×#17989685 | 2 |
| #22627098 | 2 |
| #22627007 | 2 |
| C2×#17989618 | 2 |
| #12985 | 73 |