Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
5872 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D31 |
| commutator, cosocle | C2×C31 | C26 |
| Frattini | C2 | C25×D31 |
| Fitting | C2×C31×2−1+4 | C2 |
| socle | C22×C31 | C25 |
| hypercenter | C2×2−1+4 | D31 |
| hypocenter | C31 | C22×2−1+4 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11758564 | C2 | semidirect |
| 2. C2×#11758567 | C2 | semidirect |
| 3. 2−1+4×D31 | C2 | direct (N × H) |
| 4. C2×#41×D31 | C2 | semidirect |
| 5. C22×Q8×D31 | C2 | semidirect |
| 6. C2×C31×2−1+4 | C2 | semidirect |
| 7. C31×2−1+4 | C22 | semidirect |
| 8. C2×#41×C31 | C22 | semidirect |
| 9. C22×Q8×C31 | C22 | semidirect |
| 10. #11758567 | C22 | semidirect |
| 11. #41×D31 | C22 | semidirect |
| 12. #11758564 | C22 | semidirect |
| 13. C2×#92499 | C22 | semidirect |
| 15. C2×Q8×D31 | C22 | semidirect |
| 16. C2×Q8×D31 | C22 | semidirect |
| 17. C2×#92497 | C22 | semidirect |
| 19. C2×#92495 | C22 | semidirect |
| 21. C22×Dic62 | C22 | semidirect |
| 23. #41×C31 | C23 | semidirect |
| 25. C2×Q8×C31 | C23 | semidirect |
| 30. #92499 | C23 | semidirect |
| 32. Q8×D31 | C23 | semidirect |
| 33. #92497 | C23 | semidirect |
| 35. #92495 | C23 | semidirect |
| 41. C2×Dic62 | C23 | semidirect |
| 64. C2×D31 | 2−1+4 | direct (N × H) |
| 72. C2×2−1+4 | D31 | direct (N × H) |
| 76. C2×C31 | C2×2−1+4 | semidirect |
| 79. D31 | C2×2−1+4 | direct (N × H) |
| 82. 2−1+4 | C2×D31 | direct (N × H) |
| 87. C2×#41 | C2×D31 | semidirect |
| 92. C22×Q8 | C2×D31 | semidirect |
| 95. C31 | C22×2−1+4 | semidirect |
| 100. #41 | C22×D31 | semidirect |
| 106. C2×Q8 | C22×D31 | semidirect |
| 145. C2 | 2−1+4×D31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758564 | 2 |
| C2×#11758567 | 2 |
| 2−1+4×D31 | 2 |
| C2×#41×D31 | 2 |
| C22×Q8×D31 | 2 |
| C2×C31×2−1+4 | 2 |
| C22×2−1+4 | 31 |