Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
4070 conjugacy classes of subgroups; only the 702 normal subgroups are shown.
This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 702 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C41 | C23 |
| commutator | C23 | C23×C4×C41 |
| Frattini, cosocle | C22×C4 | C24×C41 |
| socle | C24×C41 | C22×C4 |
| prime radical | C23×#41×C41 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C22⋊C8×C41 | C2 | semidirect |
| 3. C41×#1780 | C2 | direct (N × H) |
| 12. C2×C22⋊C8×C41 | C22 | semidirect |
| 76. C2×#1780 | C41 | direct (N × H) |
| 89. C22×C22⋊C8 | C2×C41 | semidirect |
| 90. #1780 | C2×C41 | direct (N × H) |
| 92. C2×C41 | #1780 | direct (N × H) |
| 103. C2×C22⋊C8 | C22×C41 | semidirect |
| 104. C41 | C2×#1780 | direct (N × H) |
| 180. C2 | C41×#1780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#41×C41 | 2 |
| C22×C22⋊C8×C41 | 2 |
| C41×#1780 | 2 |
| C2×#1780 | 41 |