Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #1304 |
| commutator | C24 | C42×C41 |
| Frattini, cosocle | C22×#41 | C22×C41 |
| prime radical | C22×#41×C41 | C22 |
| LCS | G ▷ C24 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C23×C41 ◁ C22×#41×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C2×#100×C41 | C4 | semidirect |
| 12. C41×#407 | C4 | semidirect |
| 110. #7312 | C41 | direct (N × H) |
| 146. C2×#100 | C4×C41 | semidirect |
| 150. #407 | C4×C41 | semidirect |
| 152. C41 | #7312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#1785 | 2 |
| C41×#1782 | 2 |
| #7312 | 41 |