Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 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 |
|---|---|---|
| 2. #11719532 | C2 | semidirect |
| 3. #41×Dic13 | C2 | semidirect |
| 4. #11719503 | C2 | semidirect |
| 5. C2×D4×Dic13 | C2 | semidirect |
| 6. C13×H(5,𝔽2) | C4 | semidirect |
| 9. C23×Dic13 | C22 | semidirect |
| 10. C2×C22⋊Dic13 | C22 | semidirect |
| 11. Q8×Dic13 | C22 | semidirect |
| 12. Q8×Dic13 | C22 | semidirect |
| 13. D4×Dic13 | C22 | semidirect |
| 14. D4×Dic13 | C22 | semidirect |
| 15. D4×Dic13 | C22 | semidirect |
| 16. #88180 | C22 | semidirect |
| 17. C2×C4⋊Dic13 | C22 | semidirect |
| 18. C2×C4×Dic13 | C22 | semidirect |
| 20. C13×#41 | C2×C4 | semidirect |
| 22. C2×D4×C13 | C2×C4 | semidirect |
| 37. C23×C13 | C22×C4 | semidirect |
| 39. Q8×C13 | C22×C4 | semidirect |
| 40. D4×C13 | C22×C4 | semidirect |
| 41. C2×C4×C13 | C22×C4 | semidirect |
| 62. Dic13 | H(5,𝔽2) | direct (N × H) |
| 63. H(5,𝔽2) | Dic13 | direct (N × H) |
| 81. #41 | C2×Dic13 | semidirect |
| 83. C2×D4 | C2×Dic13 | semidirect |
| 95. C13 | C4×H(5,𝔽2) | semidirect |
| 98. C23 | C22×Dic13 | semidirect |
| 100. Q8 | C22×Dic13 | semidirect |
| 101. D4 | C22×Dic13 | semidirect |
| 108. C2×C4 | C22×Dic13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(5,𝔽2) | 2 |
| #11719532 | 2 |
| #41×Dic13 | 2 |
| #11719503 | 2 |
| C2×D4×Dic13 | 2 |
| C4×H(5,𝔽2) | 13 |