Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14521680 | C2 | semidirect |
| 3. #14521412 | C2 | semidirect |
| 4. #14521407 | C2 | semidirect |
| 5. #14521402 | C2 | semidirect |
| 6. #14521394 | C2 | semidirect |
| 7. #14521054 | C2 | semidirect |
| 8. #14521048 | C2 | semidirect |
| 9. #14521046 | C2 | semidirect |
| 10. #14521004 | C2 | semidirect |
| 11. C2×C31×#102 | C2 | semidirect |
| 26. #11758467 | C22 | semidirect |
| 28. #11758465 | C22 | semidirect |
| 33. #11758409 | C22 | semidirect |
| 34. #11758409 | C22 | semidirect |
| 35. #11758404 | C22 | semidirect |
| 36. #11758404 | C22 | semidirect |
| 37. #11758403 | C22 | semidirect |
| 38. C8×Dic31 | C22 | semidirect |
| 39. #11758398 | C22 | semidirect |
| 40. #11758397 | C22 | semidirect |
| 139. C2×#102 | D31 | semidirect |
| 176. C31 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14521680 | 2 |
| #14521616 | 2 |
| #14521412 | 2 |
| #14521407 | 2 |
| #14521402 | 2 |
| #14521394 | 2 |
| #14521054 | 2 |
| #14521048 | 2 |
| #14521046 | 2 |
| #14521004 | 2 |
| C2×C31×#102 | 2 |
| #3136 | 31 |