Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
294 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C127 | #117 |
| commutator | C2×C4 | C22×C8×C127 |
| Frattini, cosocle | C22×C8 | C23×C127 |
| socle | C22×C127 | #432 |
| prime radical | C23×C127 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C127 ◁ C2×#97×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 82. #12896 | C127 | direct (N × H) |
| 91. C127 | #12896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#97×C127 | 2 |
| C127×#1377 | 2 |
| C127×#1376 | 2 |
| C127×#1375 | 2 |
| #12896 | 127 |