Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C22×#92480 | C2 | semidirect |
| 2. C2×C4×Dic62 | C2 | semidirect |
| 3. #14521246 | C2 | direct (N × H) |
| 4. C2×C4⋊(C31⋊C8) | C2 | semidirect |
| 5. C2×#11758420 | C2 | semidirect |
| 15. C2×#92480 | C22 | semidirect |
| 21. C4×Dic62 | C22 | semidirect |
| 22. #11758420 | C22 | semidirect |
| 23. C4⋊(C31⋊C8) | C22 | semidirect |
| 40. C2×Dic62 | D4 | semidirect |
| 62. C2×C4×C31 | SD16 | semidirect |
| 75. Dic62 | C2×D4 | semidirect |
| 88. C4×C31 | C2×SD16 | semidirect |
| 100. C2×C31 | #460 | semidirect |
| 121. C31 | C2×#460 | semidirect |
| 167. C2×C4 | #92480 | semidirect |
| 186. C4 | C2×#92480 | semidirect |
| 191. C2 | #14521246 | 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 |
| #14521246 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×#11758420 | 2 |
| C2×C31×#127 | 2 |
| C2×#460 | 31 |