Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1072 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 469 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. C23×C31⋊C8 | C2 | semidirect |
| 2. C2×C22⋊(C31⋊C8) | C2 | direct (N × H) |
| 11. C22×C31⋊C8 | C22 | semidirect |
| 12. C22⋊(C31⋊C8) | C22 | direct (N × H) |
| 15. C24×C31 | C8 | semidirect |
| 28. C2×C31⋊C8 | C23 | semidirect |
| 34. C23×C31 | C2×C8 | semidirect |
| 51. C22×C31 | C22⋊C8 | semidirect |
| 54. C22×C31 | C22×C8 | semidirect |
| 64. C2×C31 | C2×C22⋊C8 | semidirect |
| 77. C31 | C22×C22⋊C8 | semidirect |
| 80. C24 | C31⋊C8 | semidirect |
| 98. C23 | C2×C31⋊C8 | semidirect |
| 115. C22 | C22⋊(C31⋊C8) | direct (N × H) |
| 117. C22 | C22×C31⋊C8 | semidirect |
| 125. C2 | C2×C22⋊(C31⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C31⋊C8 | 2 |
| C2×C22⋊(C31⋊C8) | 2 |
| C24×C4×C31 | 2 |
| C22×C22⋊C8 | 31 |