Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
3422 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 3422 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D251 |
| commutator, socle, cosocle | C23×C251 | C24 |
| Fitting | #379×C251 | C2 |
| hypercenter | #379 | D251 |
| hypocenter | C251 | #2846 |
| LCS | G ▷ C23×C251 ▷ C251 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D251 | C2 | semidirect |
| 2. C2×#22548685 | C2 | semidirect |
| 3. C2×#22548684 | C2 | semidirect |
| 4. #30631542 | C2 | semidirect |
| 5. #379×C251 | C2 | semidirect |
| 9. C22×D1004 | C22 | semidirect |
| 10. C22×C22⋊D251 | C22 | semidirect |
| 13. C2×C22⋊Dic251 | C22 | semidirect |
| 14. C2×(C2×D251)⋊C4 | C22 | semidirect |
| 16. C2×C22⋊C4×C251 | C22 | semidirect |
| 22. C23×D251 | D4 | semidirect |
| 24. C23×D251 | C23 | semidirect |
| 28. C22×Dic251 | C23 | semidirect |
| 32. C24×C251 | D4 | semidirect |
| 34. C22×C4×C251 | C23 | semidirect |
| 60. C22×C251 | #120 | semidirect |
| 68. C2×D251 | #120 | semidirect |
| 76. C251 | #2846 | semidirect |
| 82. #379 | D251 | semidirect |
| 93. C2×C22⋊C4 | C2×D251 | semidirect |
| 103. C24 | D1004 | semidirect |
| 109. C22×C4 | C22×D251 | semidirect |
| 143. C22 | #22548685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D251 | 2 |
| C2×#22548685 | 2 |
| C2×#22548684 | 2 |
| #30631542 | 2 |
| #379×C251 | 2 |
| #2846 | 251 |