Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1296 conjugacy classes of subgroups; only the 517 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 517 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×D31 |
| commutator, socle, cosocle | C22×C31 | C25 |
| Fitting | C31×#543 | C2 |
| prime radical | C24×D31 | C22 |
| hypercenter | #543 | D31 |
| hypocenter | C31 | C2×#543 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #543 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14521675 | C2 | semidirect |
| 2. #14521674 | C2 | semidirect |
| 3. C22⋊Q8×D31 | C2 | semidirect |
| 5. C31×#543 | C2 | semidirect |
| 7. C2×Q8×D31 | C22 | semidirect |
| 9. C31×C22⋊Q8 | C22 | semidirect |
| 12. #11758523 | C22 | semidirect |
| 14. #11758501 | C22 | semidirect |
| 15. #11758474 | C22 | semidirect |
| 16. #11758473 | C22 | semidirect |
| 17. C4⋊C4×D31 | C22 | semidirect |
| 20. #11758455 | C22 | semidirect |
| 23. C23×D31 | Q8 | semidirect |
| 26. C2×Q8×C31 | C23 | semidirect |
| 33. C2×Dic62 | C23 | semidirect |
| 34. C4⋊C4×C31 | C23 | semidirect |
| 38. C4⋊Dic31 | C23 | semidirect |
| 39. Dic31⋊C4 | C23 | semidirect |
| 41. C23×C31 | C2×Q8 | semidirect |
| 47. C22×D31 | C2×Q8 | semidirect |
| 73. #543 | D31 | direct (N × H) |
| 80. D31 | #543 | direct (N × H) |
| 89. C22⋊Q8 | C2×D31 | semidirect |
| 96. C31 | C2×#543 | semidirect |
| 104. C2×Q8 | C22×D31 | semidirect |
| 112. C4⋊C4 | C22×D31 | semidirect |
| 124. C23 | Q8×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521675 | 2 |
| #14521674 | 2 |
| C22⋊Q8×D31 | 2 |
| C2×C22⋊C4×D31 | 2 |
| C31×#543 | 2 |
| C2×#543 | 31 |