Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#11758492 | C2 | semidirect |
| 3. C4⋊Q8×D31 | C2 | semidirect |
| 4. #14521440 | C2 | semidirect |
| 5. #14521429 | C2 | semidirect |
| 6. #14521428 | C2 | semidirect |
| 7. #14521421 | C2 | semidirect |
| 8. C4×#92469 | C2 | semidirect |
| 9. C31×#492 | C2 | semidirect |
| 59. #92469 | D4 | semidirect |
| 89. C4×C31 | #137 | semidirect |
| 102. #492 | D31 | semidirect |
| 130. C31 | #3152 | semidirect |
| 191. C4 | #11758492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758492 | 2 |
| #14521597 | 2 |
| C4⋊Q8×D31 | 2 |
| #14521440 | 2 |
| #14521429 | 2 |
| #14521428 | 2 |
| #14521421 | 2 |
| C4×#92469 | 2 |
| C31×#492 | 2 |
| #3152 | 31 |