Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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⋊(C31⋊C8) | C2 | semidirect |
| 4. #14520811 | C2 | semidirect |
| 5. C31×#384 | C2 | semidirect |
| 16. C4×D124 | C4 | semidirect |
| 75. D124 | C4⋊C4 | semidirect |
| 95. C4×C31 | #102 | semidirect |
| 104. #384 | D31 | semidirect |
| 127. C31 | #1802 | semidirect |
| 204. C4 | #11758397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D124 | 2 |
| C2×C4⋊(C31⋊C8) | 2 |
| C2×#11758397 | 2 |
| #14520811 | 2 |
| C31×#384 | 2 |
| #1802 | 31 |