Finite Group DatabasebetaFinite Group DatabasebetaOrder 32512.
2502 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C127 | C24 |
| commutator | C23 | C23×C4×C127 |
| Frattini, cosocle | C24 | C24×C127 |
| prime radical | C22×#127×C127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#383×C127 | C2 | semidirect |
| 3. C127×#1438 | C2 | semidirect |
| 6. C2×#127×C127 | C4 | semidirect |
| 35. C42×C127 | C22⋊C4 | semidirect |
| 59. #14661 | C127 | direct (N × H) |
| 65. C2×#383 | C2×C127 | semidirect |
| 66. #1438 | C2×C127 | semidirect |
| 67. C127 | #14661 | direct (N × H) |
| 70. C2×#127 | C4×C127 | semidirect |
| 99. C42 | C22⋊C4×C127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#127×C127 | 2 |
| C2×#383×C127 | 2 |
| C127×#1438 | 2 |
| #14661 | 127 |