Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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 |
| 2. C22×#92479 | C2 | semidirect |
| 3. C2×#11758451 | C2 | semidirect |
| 4. #14521439 | C2 | direct (N × H) |
| 5. C2×#11758391 | C2 | semidirect |
| 6. C2×C31×#124 | C2 | semidirect |
| 12. C31×#124 | C22 | semidirect |
| 16. C2×#92481 | C22 | semidirect |
| 18. C2×#92479 | C22 | semidirect |
| 21. #11758451 | C22 | semidirect |
| 22. #11758391 | C22 | semidirect |
| 45. C2×C31⋊C8 | D4 | semidirect |
| 69. C31⋊C8 | C2×D4 | semidirect |
| 87. C2×#124 | D31 | semidirect |
| 91. C2×C31 | #496 | semidirect |
| 107. #124 | C2×D31 | semidirect |
| 111. C31 | C2×#496 | semidirect |
| 174. C2 | #14521439 | 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×#92479 | 2 |
| C2×#11758451 | 2 |
| #14521439 | 2 |
| C2×#11758391 | 2 |
| C2×C31×#124 | 2 |
| C2×#496 | 31 |