Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 216 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×C251 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C251 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C251 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 58. C251 | #2571 | direct (N × H) |
| 59. #2571 | C251 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #400×C251 | 2 |
| #389×C251 | 2 |
| #384×C251 | 2 |
| #382×C251 | 2 |
| C4×C4⋊C4×C251 | 2 |
| #2571 | 251 |