Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C251 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C251 |
| Frattini, cosocle | C42 | C23×C251 |
| prime radical | C22×D4×C251 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C251 ◁ C2×C42×C251 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #432×C251 | C2 | semidirect |
| 3. C4×M16×C251 | C2 | semidirect |
| 4. #329×C251 | C2 | semidirect |
| 17. #97×C251 | C22 | semidirect |
| 18. #97×C251 | C22 | semidirect |
| 84. C251 | #1527 | direct (N × H) |
| 85. #1527 | C251 | direct (N × H) |
| 87. #432 | C2×C251 | semidirect |
| 88. C4×M16 | C2×C251 | semidirect |
| 89. #329 | C2×C251 | semidirect |
| 102. #97 | C22×C251 | semidirect |
| 103. #97 | C22×C251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C251 | 2 |
| #432×C251 | 2 |
| C4×M16×C251 | 2 |
| #329×C251 | 2 |
| #1527 | 251 |