Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#92481 | C2 | semidirect |
| 3. #14521249 | C2 | direct (N × H) |
| 4. C2×C4⋊(C31⋊C8) | C2 | semidirect |
| 5. C2×#11758397 | C2 | semidirect |
| 6. C2×C4×Q8×C31 | C2 | semidirect |
| 12. C4×Q8×C31 | C22 | semidirect |
| 18. C2×#92481 | C22 | semidirect |
| 22. #11758397 | C22 | semidirect |
| 23. C4⋊(C31⋊C8) | C22 | semidirect |
| 27. C2×Q8×C31 | D4 | semidirect |
| 58. Q8×C31 | C2×D4 | semidirect |
| 64. C2×C4×C31 | SD16 | semidirect |
| 90. C4×C31 | C2×SD16 | semidirect |
| 95. C2×C4×Q8 | D31 | semidirect |
| 99. C2×C31 | #460 | semidirect |
| 114. C4×Q8 | C2×D31 | semidirect |
| 121. C31 | C2×#460 | semidirect |
| 125. C2×Q8 | D124 | semidirect |
| 156. Q8 | C2×D124 | semidirect |
| 167. C2×C4 | #92481 | semidirect |
| 187. C4 | C2×#92481 | semidirect |
| 191. C2 | #14521249 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92481 | 2 |
| C2×#11758451 | 2 |
| #14521249 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×#11758397 | 2 |
| C2×C4×Q8×C31 | 2 |
| C2×#460 | 31 |