Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
1130 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 310 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C127 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C127 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. C2×C42×C127 | Q8 | semidirect |
| 89. #17053 | C127 | direct (N × H) |
| 98. C127 | #17053 | direct (N × H) |
| 115. C2×C42 | Q8×C127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C127×#1446 | 2 |
| C127×#1443 | 2 |
| C127×#1434 | 2 |
| #17053 | 127 |