Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
338 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C127 | C42 |
| commutator | C4 | C2×C4×C8×C127 |
| Frattini, cosocle | C22×C8 | C23×C127 |
| socle | C22×C127 | C2×#97 |
| prime radical | C23×C127 | C2×M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #346×C127 | C4 | semidirect |
| 11. C4×C16×C127 | C4 | semidirect |
| 62. #12593 | C127 | direct (N × H) |
| 69. C127 | #12593 | direct (N × H) |
| 76. #346 | C4×C127 | semidirect |
| 77. C4×C16 | C4×C127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×M32×C127 | 2 |
| C127×#1726 | 2 |
| C127×#1375 | 2 |
| #12593 | 127 |