Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2664 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.
This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 1093 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. #13118010 | C2 | semidirect |
| 2. #13117977 | C2 | semidirect |
| 3. #124×Dic13 | C2 | semidirect |
| 4. #120×Dic13 | C2 | semidirect |
| 6. C24×Dic13 | C22 | semidirect |
| 7. C13×H(3,𝔽4) | C4 | semidirect |
| 10. C2×Q8×Dic13 | C22 | semidirect |
| 12. #11718908 | C22 | semidirect |
| 13. #11718891 | C22 | semidirect |
| 16. #11718612 | C22 | semidirect |
| 17. #11718611 | C22 | semidirect |
| 18. C22⋊C4×Dic13 | C22 | semidirect |
| 19. #11718597 | C22 | semidirect |
| 20. C42×Dic13 | C22 | semidirect |
| 27. C13×#124 | C2×C4 | semidirect |
| 28. C13×#120 | C2×C4 | semidirect |
| 43. C24×C13 | C22×C4 | semidirect |
| 47. C2×Q8×C13 | C22×C4 | semidirect |
| 58. C13×C22⋊C4 | C22×C4 | semidirect |
| 59. C42×C13 | C22×C4 | semidirect |
| 90. H(3,𝔽4) | Dic13 | direct (N × H) |
| 114. Dic13 | H(3,𝔽4) | direct (N × H) |
| 121. #124 | C2×Dic13 | semidirect |
| 122. #120 | C2×Dic13 | semidirect |
| 140. C24 | C22×Dic13 | semidirect |
| 144. C2×Q8 | C22×Dic13 | semidirect |
| 159. C22⋊C4 | C22×Dic13 | semidirect |
| 162. C42 | C22×Dic13 | semidirect |
| 163. C13 | C4×H(3,𝔽4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13118010 | 2 |
| #13117977 | 2 |
| #124×Dic13 | 2 |
| #120×Dic13 | 2 |
| C2×C13×H(3,𝔽4) | 2 |
| C4×H(3,𝔽4) | 13 |