Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2830 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2830 conjugacy classes of subgroups — too many to draw. Only its 747 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×#14556583 | C2 | semidirect |
| 2. C2×#17988951 | C2 | direct (N × H) |
| 3. C22×#14556512 | C2 | semidirect |
| 4. C22×#14556502 | C2 | semidirect |
| 8. C2×#14556583 | C22 | semidirect |
| 11. #17988951 | C22 | direct (N × H) |
| 12. C2×#14556512 | C22 | semidirect |
| 13. C2×#14556502 | C22 | semidirect |
| 23. #14556583 | C23 | semidirect |
| 27. #14556512 | C23 | semidirect |
| 28. #14556502 | C23 | semidirect |
| 87. C22×C73 | #490 | semidirect |
| 97. C2×C73 | C2×#490 | semidirect |
| 105. C73 | C22×#490 | semidirect |
| 187. C22 | #17988951 | direct (N × H) |
| 196. C2 | C2×#17988951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556583 | 2 |
| C2×#17988951 | 2 |
| C22×#14556512 | 2 |
| C22×#14556502 | 2 |
| C22×#127×C73 | 2 |
| C22×#490 | 73 |