Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
5872 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D31 |
| commutator, cosocle | C2×C31 | C26 |
| Frattini | C2 | C25×D31 |
| Fitting | C22×#41×C31 | C2 |
| socle | C23×C31 | C24 |
| hypercenter | C22×#41 | D31 |
| hypocenter | C31 | C22×2−1+4 |
| LCS | G ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11758567 | C2 | direct (N × H) |
| 2. C22×#92495 | C2 | semidirect |
| 3. C22×#92497 | C2 | semidirect |
| 4. C23×Dic62 | C2 | semidirect |
| 5. C22×Q8×D31 | C2 | semidirect |
| 6. C22×#41×C31 | C2 | semidirect |
| 7. C2×#41×C31 | C22 | semidirect |
| 13. #11758567 | C22 | direct (N × H) |
| 14. C2×Q8×D31 | C22 | semidirect |
| 15. C2×#92497 | C22 | semidirect |
| 16. C2×#92495 | C22 | semidirect |
| 21. C22×Dic62 | C22 | semidirect |
| 24. #41×C31 | C23 | semidirect |
| 33. Q8×D31 | C23 | semidirect |
| 34. #92497 | C23 | semidirect |
| 35. #92495 | C23 | semidirect |
| 40. C2×Dic62 | C23 | semidirect |
| 60. C22×C31 | 2−1+4 | semidirect |
| 71. C22×#41 | D31 | semidirect |
| 75. C2×C31 | C2×2−1+4 | semidirect |
| 81. C2×#41 | C2×D31 | semidirect |
| 93. C31 | C22×2−1+4 | semidirect |
| 98. #41 | C22×D31 | semidirect |
| 133. C22 | #11758567 | direct (N × H) |
| 141. C2 | C2×#11758567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758567 | 2 |
| C22×#92495 | 2 |
| C22×#92497 | 2 |
| C23×Dic62 | 2 |
| C22×Q8×D31 | 2 |
| C22×#41×C31 | 2 |
| C22×2−1+4 | 31 |