Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C127 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C127 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 46. C4×C127 | #125 | semidirect |
| 52. #2859 | C127 | direct (N × H) |
| 53. C127 | #2859 | direct (N × H) |
| 99. C4 | #125×C127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#125×C127 | 2 |
| #389×C127 | 2 |
| #384×C127 | 2 |
| #382×C127 | 2 |
| C43×C127 | 2 |
| #2859 | 127 |