Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
1762 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 1762 conjugacy classes of subgroups — too many to draw. Only its 366 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, Frattini, cosocle | C24 | C24×C127 |
| prime radical | C23×D4×C127 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#396×C127 | C2 | semidirect |
| 2. C127×#1444 | C2 | semidirect |
| 20. #95×C127 | D4 | semidirect |
| 67. #17135 | C127 | direct (N × H) |
| 73. C2×#396 | C2×C127 | semidirect |
| 74. #1444 | C2×C127 | semidirect |
| 76. C127 | #17135 | direct (N × H) |
| 93. #95 | D4×C127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#396×C127 | 2 |
| C127×#1444 | 2 |
| C127×#1438 | 2 |
| #17135 | 127 |