Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic62 | C2 | semidirect |
| 3. #14521149 | C2 | direct (N × H) |
| 4. C2×#11758395 | C2 | semidirect |
| 5. C2×#11758398 | C2 | semidirect |
| 7. C2×#11758391 | C2 | semidirect |
| 17. C2×#92480 | C4 | semidirect |
| 25. C4×Dic62 | C22 | semidirect |
| 27. #11758398 | C22 | semidirect |
| 28. #11758395 | C22 | semidirect |
| 29. #11758391 | C22 | semidirect |
| 45. C2×Dic62 | C2×C4 | semidirect |
| 52. #92480 | C2×C4 | semidirect |
| 58. C2×C31⋊C8 | C2×C4 | semidirect |
| 86. Dic62 | C22×C4 | semidirect |
| 88. C31⋊C8 | C22×C4 | semidirect |
| 115. C2×C31 | #440 | semidirect |
| 140. C31 | C2×#440 | semidirect |
| 217. C2 | #14521149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92480 | 2 |
| C2×C4×Dic62 | 2 |
| #14521149 | 2 |
| C2×#11758395 | 2 |
| C2×#11758398 | 2 |
| C2×#11758420 | 2 |
| C2×#11758391 | 2 |
| C2×C4×D4×C31 | 2 |
| C2×#440 | 31 |