Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×D4×Dic31 | C2 | semidirect |
| 3. C2×#11758470 | C2 | semidirect |
| 4. #14521158 | C2 | direct (N × H) |
| 5. C2×#11758396 | C2 | semidirect |
| 6. C2×#11758409 | C2 | semidirect |
| 7. C2×#11758403 | C2 | semidirect |
| 8. C2×C31×#102 | C2 | semidirect |
| 17. D4×Dic31 | C22 | semidirect |
| 18. C2×#92479 | C4 | semidirect |
| 25. #11758470 | C22 | semidirect |
| 26. C31×#102 | C22 | semidirect |
| 27. #11758409 | C22 | semidirect |
| 28. #11758403 | C22 | semidirect |
| 29. #11758396 | C22 | semidirect |
| 34. C2×D4×C31 | C2×C4 | semidirect |
| 45. C2×D124 | C2×C4 | semidirect |
| 54. #92479 | C2×C4 | semidirect |
| 60. C2×C31⋊C8 | C2×C4 | semidirect |
| 73. D4×C31 | C22×C4 | semidirect |
| 89. D124 | C22×C4 | semidirect |
| 92. C31⋊C8 | C22×C4 | semidirect |
| 119. C2×#102 | D31 | semidirect |
| 122. C2×C31 | #442 | semidirect |
| 146. #102 | C2×D31 | semidirect |
| 148. C31 | C2×#442 | semidirect |
| 157. C2×D4 | C4×D31 | semidirect |
| 195. D4 | C2×C4×D31 | semidirect |
| 233. C2 | #14521158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92479 | 2 |
| C2×D4×Dic31 | 2 |
| C2×#11758470 | 2 |
| #14521158 | 2 |
| C2×#11758396 | 2 |
| C2×#11758409 | 2 |
| C2×#11758403 | 2 |
| C2×C31×#102 | 2 |
| C2×#442 | 31 |