Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C2×#11758484 | C2 | semidirect |
| 3. #14521170 | C2 | direct (N × H) |
| 4. C2×#11758413 | C2 | semidirect |
| 5. C2×#11758403 | C2 | semidirect |
| 6. C2×C31×#108 | C2 | semidirect |
| 13. #11758484 | C22 | semidirect |
| 14. C2×Dic124 | C4 | semidirect |
| 15. #11758481 | C4 | semidirect |
| 17. C2×D248 | C4 | semidirect |
| 18. C2×#92470 | C4 | semidirect |
| 21. C31×#108 | C22 | semidirect |
| 22. #11758413 | C22 | semidirect |
| 23. #11758403 | C22 | semidirect |
| 46. Dic124 | C2×C4 | semidirect |
| 47. D248 | C2×C4 | semidirect |
| 48. #92470 | C2×C4 | semidirect |
| 90. C2×#108 | D31 | semidirect |
| 95. C2×C31 | #444 | semidirect |
| 112. #108 | C2×D31 | semidirect |
| 115. C31 | C2×#444 | semidirect |
| 181. C2 | #14521170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11758481 | 2 |
| C2×#11758484 | 2 |
| #14521170 | 2 |
| C2×#11758413 | 2 |
| C2×#11758403 | 2 |
| C2×C31×#108 | 2 |
| C2×#444 | 31 |