Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 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 | C22×C31 | C25 |
| Frattini | C22 | C24×D31 |
| Fitting | C22×#41×C31 | C2 |
| socle | C23×C31 | C24 |
| hypercenter | C22×#41 | D31 |
| hypocenter | C31 | C2×#550 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#92499 | C2 | semidirect |
| 2. #14521718 | C2 | direct (N × H) |
| 3. C2×#11758517 | C2 | semidirect |
| 4. C2×#11758507 | C2 | semidirect |
| 5. C2×#11758515 | C2 | semidirect |
| 6. C2×Q8×Dic31 | C2 | semidirect |
| 7. C2×C4×C22⋊D31 | C2 | semidirect |
| 8. C22×#41×C31 | C2 | semidirect |
| 10. C2×#41×C31 | C22 | semidirect |
| 17. C2×#92499 | C22 | semidirect |
| 21. Q8×Dic31 | C22 | semidirect |
| 22. #11758517 | C22 | semidirect |
| 23. #11758515 | C22 | semidirect |
| 24. #11758507 | C22 | semidirect |
| 25. C4×C22⋊D31 | C22 | semidirect |
| 33. C2×Q8×C31 | D4 | semidirect |
| 67. Q8×C31 | C2×D4 | semidirect |
| 78. C2×Dic31 | #41 | semidirect |
| 101. Dic31 | C2×#41 | semidirect |
| 103. C22×#41 | D31 | semidirect |
| 111. C2×C31 | #550 | semidirect |
| 119. C2×#41 | C2×D31 | semidirect |
| 137. C31 | C2×#550 | semidirect |
| 142. C2×Q8 | C22⋊D31 | semidirect |
| 175. Q8 | C2×C22⋊D31 | semidirect |
| 211. C2 | #14521718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92499 | 2 |
| #14521718 | 2 |
| C2×#11758517 | 2 |
| C2×#11758507 | 2 |
| C2×#11758515 | 2 |
| C2×Q8×Dic31 | 2 |
| C2×C4×C22⋊D31 | 2 |
| C22×#41×C31 | 2 |
| C2×#550 | 31 |