Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
694 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C41 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C41×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 96. #33093 | C41 | direct (N × H) |
| 135. C41 | #33093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2645 | 2 |
| C41×#2276 | 2 |
| C41×#1928 | 2 |
| C41×#1918 | 2 |
| C41×#1878 | 2 |
| C41×#1863 | 2 |
| C41×#1840 | 2 |
| #33093 | 41 |