Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11758524 | C2 | semidirect |
| 4. #14521434 | C2 | direct (N × H) |
| 5. C2×C8×Dic31 | C2 | semidirect |
| 6. C22×Q16×C31 | C2 | semidirect |
| 10. C2×Q16×C31 | C22 | semidirect |
| 13. #11758524 | C22 | semidirect |
| 15. C2×#92481 | C22 | semidirect |
| 21. C8×Dic31 | C22 | semidirect |
| 76. C22×Q16 | D31 | semidirect |
| 82. C2×C31 | #495 | semidirect |
| 89. C2×Q16 | C2×D31 | semidirect |
| 101. C31 | C2×#495 | semidirect |
| 156. C2 | #14521434 | 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 |
| C22×D248 | 2 |
| C2×#11758524 | 2 |
| #14521434 | 2 |
| C2×C8×Dic31 | 2 |
| C22×Q16×C31 | 2 |
| C2×#495 | 31 |