Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14521599 | C2 | semidirect |
| 2. #14521367 | C2 | semidirect |
| 3. #14521339 | C2 | semidirect |
| 4. #14521244 | C2 | semidirect |
| 5. #14521183 | C2 | semidirect |
| 6. #14521159 | C2 | semidirect |
| 7. #14521106 | C2 | semidirect |
| 8. C2×C4×D4×C31 | C2 | semidirect |
| 23. #11758451 | C22 | semidirect |
| 25. C4×D124 | C22 | semidirect |
| 26. #11758446 | C22 | semidirect |
| 29. #11758397 | C22 | semidirect |
| 30. #11758396 | C22 | semidirect |
| 31. C4⋊(C31⋊C8) | C22 | semidirect |
| 32. #11758391 | C22 | semidirect |
| 73. D4×C31 | #41 | semidirect |
| 116. C2×C4×D4 | D31 | semidirect |
| 153. C31 | #3109 | semidirect |
| 199. D4 | #92495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521599 | 2 |
| #14521367 | 2 |
| #14521339 | 2 |
| #14521244 | 2 |
| #14521183 | 2 |
| #14521159 | 2 |
| #14521106 | 2 |
| C2×C4×D4×C31 | 2 |
| #3109 | 31 |