Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1262 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1262 conjugacy classes of subgroups — too many to draw. Only its 309 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 | direct (N × H) |
| 5. C2×#14556687 | C22 | semidirect |
| 7. #17989685 | C22 | direct (N × H) |
| 16. #14556687 | C23 | semidirect |
| 110. C22×C73 | #349 | semidirect |
| 123. C2×C73 | C2×#349 | semidirect |
| 128. C73 | C22×#349 | semidirect |
| 235. C22 | #17989685 | direct (N × H) |
| 247. C2 | C2×#17989685 | direct (N × H) |
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 |
| C23×#11924037 | 2 |
| C22×#349 | 73 |