Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
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 |
|---|---|---|
| 2. #11740402 | C2 | semidirect |
| 3. Dic7×#124 | C2 | semidirect |
| 4. #11740025 | C2 | semidirect |
| 5. Dic7×#120 | C2 | semidirect |
| 6. C24×Dic7 | C22 | semidirect |
| 7. C7×H(3,𝔽4) | C4 | semidirect |
| 10. C2×Q8×Dic7 | C22 | semidirect |
| 12. #90019 | C22 | semidirect |
| 13. #90002 | C22 | semidirect |
| 16. #89723 | C22 | semidirect |
| 17. #89722 | C22 | semidirect |
| 18. C22⋊C4×Dic7 | C22 | semidirect |
| 19. #89708 | C22 | semidirect |
| 20. C42×Dic7 | C22 | semidirect |
| 28. C7×#124 | C2×C4 | semidirect |
| 29. C7×#120 | C2×C4 | semidirect |
| 48. C24×C7 | C22×C4 | semidirect |
| 52. C2×C7×Q8 | C22×C4 | semidirect |
| 63. C7×C22⋊C4 | C22×C4 | semidirect |
| 64. C42×C7 | C22×C4 | semidirect |
| 72. H(3,𝔽4) | Dic7 | direct (N × H) |
| 110. #124 | C2×Dic7 | semidirect |
| 111. #120 | C2×Dic7 | semidirect |
| 133. Dic7 | H(3,𝔽4) | direct (N × H) |
| 136. C24 | C22×Dic7 | semidirect |
| 140. C2×Q8 | C22×Dic7 | semidirect |
| 155. C22⋊C4 | C22×Dic7 | semidirect |
| 158. C42 | C22×Dic7 | semidirect |
| 181. C7 | C4×H(3,𝔽4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×H(3,𝔽4) | 2 |
| #11740402 | 2 |
| Dic7×#124 | 2 |
| #11740025 | 2 |
| Dic7×#120 | 2 |
| C4×H(3,𝔽4) | 7 |