Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
792 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 792 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 |
|---|---|---|
| 1. C22×#92481 | C2 | semidirect |
| 3. #14521188 | C2 | direct (N × H) |
| 4. C2×#11758423 | C2 | semidirect |
| 5. C2×C22⋊(C31⋊C8) | C2 | semidirect |
| 6. C23×Q8×C31 | C2 | semidirect |
| 11. C22×Q8×C31 | C22 | semidirect |
| 17. C2×#92481 | C22 | semidirect |
| 23. #11758423 | C22 | semidirect |
| 24. C22⋊(C31⋊C8) | C22 | semidirect |
| 33. C2×Q8×C31 | D4 | semidirect |
| 57. C23×C31 | SD16 | semidirect |
| 67. Q8×C31 | C2×D4 | semidirect |
| 90. C22×C31 | C2×SD16 | semidirect |
| 102. C23×Q8 | D31 | semidirect |
| 109. C2×C31 | #448 | semidirect |
| 118. C22×Q8 | C2×D31 | semidirect |
| 132. C31 | C2×#448 | semidirect |
| 141. C2×Q8 | C22⋊D31 | semidirect |
| 169. C23 | #92481 | semidirect |
| 175. Q8 | C2×C22⋊D31 | semidirect |
| 200. C22 | C2×#92481 | semidirect |
| 211. C2 | #14521188 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92481 | 2 |
| C2×#11758507 | 2 |
| #14521188 | 2 |
| C2×#11758423 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C23×Q8×C31 | 2 |
| C2×#448 | 31 |