Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. #11719631 | C2 | semidirect |
| 3. D13⋊#131 | C2 | semidirect |
| 4. #11719165 | C2 | semidirect |
| 5. #11719164 | C2 | semidirect |
| 6. #11719138 | C2 | semidirect |
| 7. C2×#88115 | C2 | semidirect |
| 8. C13×H(5,𝔽2) | C4 | semidirect |
| 10. #88256 | C4 | semidirect |
| 11. #88256 | C4 | semidirect |
| 16. #88251 | C4 | semidirect |
| 23. #88237 | C22 | semidirect |
| 24. C2×C4⋊#261 | C22 | semidirect |
| 25. D13⋊M16 | C22 | semidirect |
| 26. C2×D13⋊C8 | C22 | semidirect |
| 27. #88117 | C22 | semidirect |
| 28. #88117 | C22 | semidirect |
| 29. #88115 | C22 | semidirect |
| 30. #88115 | C22 | semidirect |
| 31. #88115 | C22 | semidirect |
| 36. C13×#41 | C2×C4 | semidirect |
| 38. C2×D4×C13 | C2×C4 | semidirect |
| 42. #6131 | C2×C4 | semidirect |
| 48. #6129 | C2×C4 | semidirect |
| 56. D4×D13 | C2×C4 | semidirect |
| 62. #6127 | C2×C4 | semidirect |
| 64. C2×D52 | C2×C4 | semidirect |
| 152. H(5,𝔽2) | #261 | semidirect |
| 192. #41 | C2×#261 | semidirect |
| 209. C2×D4 | C2×#261 | semidirect |
| 224. C13 | #2897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×H(5,𝔽2) | 2 |
| #11719631 | 2 |
| D13⋊#131 | 2 |
| #11719165 | 2 |
| #11719164 | 2 |
| #11719138 | 2 |
| C2×#88115 | 2 |
| #2897 | 13 |