Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
172 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #1675 |
| commutator, Frattini, cosocle | C4×C8 | C23×C127 |
| prime radical | #135×C127 | D4 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C127×#2253 | C2 | semidirect |
| 4. C127×#1373 | C2 | semidirect |
| 5. C127×#1366 | C2 | semidirect |
| 67. #12463 | C127 | direct (N × H) |
| 71. #2253 | C2×C127 | semidirect |
| 74. #1373 | C2×C127 | semidirect |
| 75. #1366 | C2×C127 | semidirect |
| 76. C127 | #12463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C127×#2253 | 2 |
| C127×#2231 | 2 |
| C127×#2170 | 2 |
| C127×#1373 | 2 |
| C127×#1366 | 2 |
| #12463 | 127 |