Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11758486 | C2 | semidirect |
| 3. C2×#11758446 | C2 | semidirect |
| 4. #14521443 | C2 | semidirect |
| 5. #14521429 | C2 | semidirect |
| 6. #14521422 | C2 | semidirect |
| 7. C4×M16×C31 | C2 | semidirect |
| 38. M16×C31 | D4 | semidirect |
| 76. C4×C31 | #137 | semidirect |
| 86. C4×M16 | D31 | semidirect |
| 109. C31 | #3152 | semidirect |
| 124. M16 | D124 | semidirect |
| 161. C4 | #11758486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758486 | 2 |
| #14521599 | 2 |
| C2×#11758446 | 2 |
| #14521443 | 2 |
| #14521429 | 2 |
| #14521422 | 2 |
| C4×M16×C31 | 2 |
| #3152 | 31 |