Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 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. #14521048 | C2 | direct (N × H) |
| 4. C2×#11758398 | C2 | semidirect |
| 5. C2×#11758397 | C2 | semidirect |
| 6. C22×C4⋊C4×C31 | C2 | semidirect |
| 12. C2×#92495 | C4 | semidirect |
| 20. C2×C4⋊C4×C31 | C22 | semidirect |
| 22. C2×#92474 | C22 | semidirect |
| 24. #11758398 | C22 | semidirect |
| 25. #11758397 | C22 | semidirect |
| 42. #92495 | C2×C4 | semidirect |
| 45. C2×D124 | C2×C4 | semidirect |
| 51. C2×Dic62 | C2×C4 | semidirect |
| 85. D124 | C22×C4 | semidirect |
| 89. Dic62 | C22×C4 | semidirect |
| 112. C22×C4⋊C4 | D31 | semidirect |
| 117. C2×C31 | #417 | semidirect |
| 138. C2×C4⋊C4 | C2×D31 | semidirect |
| 141. C31 | C2×#417 | semidirect |
| 227. C2 | #14521048 | 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 |
| #14521048 | 2 |
| C2×#11758398 | 2 |
| C2×#11758397 | 2 |
| C22×C4⋊C4×C31 | 2 |
| C2×#417 | 31 |