Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
130 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C127 | #1361 |
| commutator | C2×C16 | C2×C4×C127 |
| Frattini, cosocle | C4×C16 | C22×C127 |
| prime radical | C2×D16×C127 | C4 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ C4×C16×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C127×#1422 | C2 | semidirect |
| 3. C127×#1373 | C2 | semidirect |
| 59. #7447 | C127 | direct (N × H) |
| 64. #1422 | C2×C127 | semidirect |
| 65. #1373 | C2×C127 | semidirect |
| 66. C127 | #7447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C127×#2249 | 2 |
| C127×#1422 | 2 |
| C127×#1373 | 2 |
| #7447 | 127 |