Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C251 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C251 |
| prime radical | C25×C251 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C251 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #397×C251 | C2 | semidirect |
| 2. #393×C251 | C2 | semidirect |
| 3. #388×C251 | C2 | semidirect |
| 6. C22×Q8×C251 | C22 | semidirect |
| 7. C2×C4⋊C4×C251 | C22 | semidirect |
| 12. C2×C42×C251 | C22 | semidirect |
| 13. #95×C251 | C22 | semidirect |
| 14. #95×C251 | C22 | semidirect |
| 15. #95×C251 | C22 | semidirect |
| 63. C251 | #2736 | direct (N × H) |
| 64. #2736 | C251 | direct (N × H) |
| 65. #397 | C2×C251 | semidirect |
| 66. #393 | C2×C251 | semidirect |
| 67. #388 | C2×C251 | semidirect |
| 70. C22×Q8 | C22×C251 | semidirect |
| 71. C2×C4⋊C4 | C22×C251 | semidirect |
| 76. C2×C42 | C22×C251 | semidirect |
| 77. #95 | C22×C251 | semidirect |
| 78. #95 | C22×C251 | semidirect |
| 79. #95 | C22×C251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #397×C251 | 2 |
| #393×C251 | 2 |
| #388×C251 | 2 |
| #379×C251 | 2 |
| #2736 | 251 |