Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
198 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #340 |
| commutator | C2×C8 | C42×C127 |
| Frattini, cosocle | C2×C4×C8 | C22×C127 |
| prime radical | C23×C127 | #106 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 76. #7243 | C127 | direct (N × H) |
| 84. C127 | #7243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C16×C127 | 2 |
| C127×#1568 | 2 |
| C127×#1566 | 2 |
| #7243 | 127 |