Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
152 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | #331 |
| commutator | C4×C8 | C2×C4×C127 |
| Frattini, cosocle | C82 | C22×C127 |
| prime radical | #493×C127 | C4 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C127×#1367 | C2 | semidirect |
| 46. #7092 | C127 | direct (N × H) |
| 51. #1367 | C2×C127 | semidirect |
| 52. C127 | #7092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C127×#1709 | 2 |
| C127×#1367 | 2 |
| #7092 | 127 |