Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14521596 | C2 | semidirect |
| 2. #14521453 | C2 | semidirect |
| 3. #14521424 | C2 | semidirect |
| 4. #14521394 | C2 | semidirect |
| 5. #14521286 | C2 | semidirect |
| 6. #14521284 | C2 | semidirect |
| 7. #14521282 | C2 | semidirect |
| 8. C4×D248 | C2 | semidirect |
| 9. C4×#92479 | C2 | semidirect |
| 10. C4×C8×D31 | C2 | semidirect |
| 11. C4×D8×C31 | C2 | semidirect |
| 96. C4×D31 | D8 | semidirect |
| 99. C8×C31 | #41 | semidirect |
| 101. C31⋊C8 | #41 | semidirect |
| 131. C4×D8 | D31 | semidirect |
| 166. C31 | #3169 | semidirect |
| 229. C8 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521596 | 2 |
| #14521453 | 2 |
| #14521424 | 2 |
| #14521394 | 2 |
| #14521286 | 2 |
| #14521284 | 2 |
| #14521282 | 2 |
| C4×D248 | 2 |
| C4×#92479 | 2 |
| C4×C8×D31 | 2 |
| C4×D8×C31 | 2 |
| #3169 | 31 |