Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521772 | C2 | semidirect |
| 2. #14521411 | C2 | semidirect |
| 3. #14521401 | C2 | semidirect |
| 4. #14521341 | C2 | semidirect |
| 5. #14521326 | C2 | semidirect |
| 7. #14521254 | C2 | semidirect |
| 8. #14521180 | C2 | semidirect |
| 9. #14521149 | C2 | semidirect |
| 11. D4×Q8×C31 | C2 | semidirect |
| 119. D4×Q8 | D31 | semidirect |
| 163. C31 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521772 | 2 |
| #14521411 | 2 |
| #14521401 | 2 |
| #14521341 | 2 |
| #14521326 | 2 |
| #14521264 | 2 |
| #14521254 | 2 |
| #14521180 | 2 |
| #14521149 | 2 |
| C4×#92479 | 2 |
| D4×Q8×C31 | 2 |
| #3367 | 31 |