Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1174 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1174 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×#14556688 | C2 | semidirect |
| 2. C22×#14556686 | C2 | semidirect |
| 3. C2×#17989688 | C2 | direct (N × H) |
| 6. C2×#14556688 | C22 | semidirect |
| 8. C2×#14556686 | C22 | semidirect |
| 11. #17989688 | C22 | direct (N × H) |
| 22. #14556688 | C23 | semidirect |
| 24. #14556686 | C23 | semidirect |
| 123. C22×C73 | #350 | semidirect |
| 137. C2×C73 | C2×#350 | semidirect |
| 146. C73 | C22×#350 | semidirect |
| 271. C22 | #17989688 | direct (N × H) |
| 281. C2 | C2×#17989688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556688 | 2 |
| C22×#14556686 | 2 |
| C2×#17989688 | 2 |
| C22×#14556679 | 2 |
| C22×#350 | 73 |