Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
300 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 120 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×C257 | C2×D4 |
| commutator | C2×C4 | C22×C4×C257 |
| Frattini, cosocle | C22×C4 | C23×C257 |
| prime radical | C24×C257 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C257 ◁ C23×C4×C257 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #340×C257 | C2 | semidirect |
| 5. #340×C257 | C2 | semidirect |
| 9. #117×C257 | C4 | semidirect |
| 81. C257 | #1825 | direct (N × H) |
| 82. #1825 | C257 | direct (N × H) |
| 86. #340 | C2×C257 | semidirect |
| 87. #340 | C2×C257 | semidirect |
| 91. #117 | C4×C257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#117×C257 | 2 |
| C2×C22⋊C8×C257 | 2 |
| #380×C257 | 2 |
| #340×C257 | 2 |
| #1825 | 257 |