Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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×C257 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C257 |
| prime radical | #459×C257 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C257 ◁ C42×C257 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #486×C257 | C2 | semidirect |
| 2. #476×C257 | C2 | semidirect |
| 4. #436×C257 | C2 | semidirect |
| 5. #335×C257 | C2 | semidirect |
| 6. #333×C257 | C2 | semidirect |
| 7. #331×C257 | C2 | semidirect |
| 82. C257 | #1697 | direct (N × H) |
| 83. #1697 | C257 | direct (N × H) |
| 84. #486 | C2×C257 | semidirect |
| 85. #476 | C2×C257 | semidirect |
| 87. #436 | C2×C257 | semidirect |
| 88. #335 | C2×C257 | semidirect |
| 89. #333 | C2×C257 | semidirect |
| 90. #331 | C2×C257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #486×C257 | 2 |
| #476×C257 | 2 |
| #459×C257 | 2 |
| #436×C257 | 2 |
| #335×C257 | 2 |
| #333×C257 | 2 |
| #331×C257 | 2 |
| #1697 | 257 |