Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
526 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C127 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C127 |
| prime radical | C2×#127×C127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C127×#1845 | C2 | semidirect |
| 3. C127×#1273 | C2 | semidirect |
| 55. #10673 | C127 | direct (N × H) |
| 61. #1845 | C2×C127 | semidirect |
| 62. #1273 | C2×C127 | semidirect |
| 63. C127 | #10673 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C127×#1957 | 2 |
| C127×#1845 | 2 |
| C127×#1273 | 2 |
| #10673 | 127 |