Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#92474 | C2 | semidirect |
| 3. C2×#11758393 | C2 | direct (N × H) |
| 4. C22×C42×C31 | C2 | semidirect |
| 10. C2×#92495 | C4 | semidirect |
| 12. C22×D124 | C4 | semidirect |
| 14. C22×Dic62 | C4 | semidirect |
| 16. C2×C42×C31 | C22 | semidirect |
| 18. C2×#92474 | C22 | semidirect |
| 20. #11758393 | C22 | direct (N × H) |
| 37. #92495 | C2×C4 | semidirect |
| 40. C2×D124 | C2×C4 | semidirect |
| 44. C2×Dic62 | C2×C4 | semidirect |
| 46. C42×C31 | C23 | semidirect |
| 48. #92474 | C23 | semidirect |
| 71. D124 | C22×C4 | semidirect |
| 75. Dic62 | C22×C4 | semidirect |
| 80. C22×C31 | #104 | semidirect |
| 94. C22×C42 | D31 | semidirect |
| 98. C2×C31 | C2×#104 | semidirect |
| 115. C2×C42 | C2×D31 | semidirect |
| 117. C31 | C22×#104 | semidirect |
| 146. C42 | C22×D31 | semidirect |
| 178. C22 | #11758393 | direct (N × H) |
| 191. C2 | C2×#11758393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92495 | 2 |
| C22×#92474 | 2 |
| C2×#11758393 | 2 |
| C22×C42×C31 | 2 |
| C22×#104 | 31 |