Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
2302 conjugacy classes of subgroups; only the 1534 normal subgroups are shown.
This group has 2302 conjugacy classes of subgroups — too many to draw. Only its 1534 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C42×C127 | C22 |
| commutator | C2 | C2×C43×C127 |
| Frattini, cosocle | C24 | C24×C127 |
| socle, prime radical | C24×C127 | C24 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #376×C127 | C4 | direct (N × H) |
| 9. C43×C127 | C4 | semidirect |
| 29. C42×C127 | C42 | semidirect |
| 46. C4×C127 | #376 | direct (N × H) |
| 47. C4×#376 | C127 | direct (N × H) |
| 54. C127 | C4×#376 | direct (N × H) |
| 58. #376 | C4×C127 | direct (N × H) |
| 60. C43 | C4×C127 | semidirect |
| 80. C42 | C42×C127 | semidirect |
| 97. C4 | #376×C127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#376×C127 | 2 |
| C2×C43×C127 | 2 |
| C4×#95×C127 | 2 |
| C4×#376 | 127 |