Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1408 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 459 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D29 |
| commutator, socle, cosocle | C22×C29 | C25 |
| Fitting | C29×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D29 |
| hypocenter | C29 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271906 | C2 | semidirect |
| 2. #14271905 | C2 | semidirect |
| 3. #124×D29 | C2 | semidirect |
| 4. #120×D29 | C2 | semidirect |
| 5. C29×H(3,𝔽4) | C2 | semidirect |
| 6. C24×D29 | C22 | semidirect |
| 7. C2×Q8×D29 | C22 | semidirect |
| 9. C29×#124 | C22 | semidirect |
| 10. C29×#120 | C22 | semidirect |
| 11. #11745315 | C22 | semidirect |
| 12. #11745309 | C22 | semidirect |
| 13. #11745299 | C22 | semidirect |
| 14. #11745298 | C22 | semidirect |
| 15. #11745247 | C22 | semidirect |
| 16. #11745244 | C22 | semidirect |
| 17. C22⋊C4×D29 | C22 | semidirect |
| 18. #11745237 | C22 | semidirect |
| 19. C42×D29 | C22 | semidirect |
| 20. C24×C29 | C23 | semidirect |
| 23. C23×D29 | C23 | semidirect |
| 24. C2×Q8×C29 | C23 | semidirect |
| 31. C2×Dic58 | C23 | semidirect |
| 32. C22⋊C4×C29 | C23 | semidirect |
| 33. C42×C29 | C23 | semidirect |
| 34. C22⋊Dic29 | C23 | semidirect |
| 35. #90781 | C23 | semidirect |
| 36. C4×Dic29 | C23 | semidirect |
| 64. H(3,𝔽4) | D29 | direct (N × H) |
| 70. D29 | H(3,𝔽4) | direct (N × H) |
| 78. #124 | C2×D29 | semidirect |
| 82. #120 | C2×D29 | semidirect |
| 85. C29 | C2×H(3,𝔽4) | semidirect |
| 89. C24 | C22×D29 | semidirect |
| 92. C2×Q8 | C22×D29 | semidirect |
| 100. C22⋊C4 | C22×D29 | semidirect |
| 102. C42 | C22×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271906 | 2 |
| #14271905 | 2 |
| #124×D29 | 2 |
| #120×D29 | 2 |
| C29×H(3,𝔽4) | 2 |
| C2×H(3,𝔽4) | 29 |