Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
4462 conjugacy classes of subgroups; only the 1214 normal subgroups are shown.
This group has 4462 conjugacy classes of subgroups — too many to draw. Only its 1214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C127 | C24 |
| commutator | C22 | C22×C42×C127 |
| Frattini, cosocle | C24 | C24×C127 |
| prime radical | C26×C127 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C127×C22⋊#95 | C2 | semidirect |
| 6. C22×C22⋊C4×C127 | C4 | semidirect |
| 8. C2×#95×C127 | C22 | semidirect |
| 16. C23×C4×C127 | C2×C4 | semidirect |
| 21. C2×C22⋊C4×C127 | C2×C4 | semidirect |
| 51. C23×C127 | #95 | semidirect |
| 79. #13794 | C127 | direct (N × H) |
| 86. C22⋊#95 | C2×C127 | semidirect |
| 87. C127 | #13794 | direct (N × H) |
| 91. C22×C22⋊C4 | C4×C127 | semidirect |
| 93. C2×#95 | C22×C127 | semidirect |
| 101. C23×C4 | C2×C4×C127 | semidirect |
| 106. C2×C22⋊C4 | C2×C4×C127 | semidirect |
| 136. C23 | #95×C127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊C4×C127 | 2 |
| C127×C22⋊#95 | 2 |
| #13794 | 127 |