Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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. #14521613 | C2 | semidirect |
| 2. C2×#11758517 | C2 | semidirect |
| 3. C2×#11758425 | C2 | semidirect |
| 4. #14521054 | C2 | semidirect |
| 5. C2×#11758411 | C2 | semidirect |
| 6. #14520810 | C2 | semidirect |
| 7. C2×C31×AGL(1,ℤ/8) | C2 | semidirect |
| 35. C2×Q8×C31 | D4 | semidirect |
| 42. C2×D4×C31 | D4 | semidirect |
| 43. C2×D4×C31 | D4 | semidirect |
| 59. M16×C31 | D4 | semidirect |
| 63. C4⋊Dic31 | D4 | semidirect |
| 66. C4×Dic31 | D4 | semidirect |
| 132. C2×AGL(1,ℤ/8) | D31 | semidirect |
| 167. C31 | #2002 | semidirect |
| 174. C2×Q8 | C22⋊D31 | semidirect |
| 190. C2×D4 | C22⋊D31 | semidirect |
| 191. C2×D4 | C22⋊D31 | semidirect |
| 200. M16 | C22⋊D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521613 | 2 |
| C2×#11758517 | 2 |
| C2×#11758425 | 2 |
| #14521054 | 2 |
| C2×#11758411 | 2 |
| #14520810 | 2 |
| C2×C31×AGL(1,ℤ/8) | 2 |
| #2002 | 31 |