Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D31 | C2 | semidirect |
| 3. #14521429 | C2 | semidirect |
| 4. #14521291 | C2 | semidirect |
| 5. #14521259 | C2 | semidirect |
| 6. #14521206 | C2 | semidirect |
| 8. C4×Q16×C31 | C2 | semidirect |
| 37. Q16×C31 | D4 | semidirect |
| 65. D124 | Q16 | direct (N × H) |
| 79. C2×D31 | C2×Q16 | semidirect |
| 83. C4×C31 | C2×Q16 | semidirect |
| 94. C4×Q16 | D31 | semidirect |
| 120. C31 | D4×Q16 | semidirect |
| 132. Q16 | D124 | direct (N × H) |
| 176. C4 | Q16×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D31 | 2 |
| Q8×D124 | 2 |
| #14521429 | 2 |
| #14521291 | 2 |
| #14521259 | 2 |
| #14521206 | 2 |
| C8×D124 | 2 |
| C4×Q16×C31 | 2 |
| D4×Q16 | 31 |