Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1494 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 310 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×C41 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ C22×#41×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#131×C41 | C2 | semidirect |
| 2. C2×C41×#466 | C2 | semidirect |
| 3. C41×#2615 | C2 | semidirect |
| 4. C41×#1895 | C2 | semidirect |
| 5. C41×#1808 | C2 | semidirect |
| 31. C22×C8×C41 | D4 | semidirect |
| 95. #32933 | C41 | direct (N × H) |
| 111. C22×#131 | C2×C41 | semidirect |
| 112. C2×#466 | C2×C41 | semidirect |
| 113. #2615 | C2×C41 | semidirect |
| 114. #1895 | C2×C41 | semidirect |
| 115. #1808 | C2×C41 | semidirect |
| 134. C41 | #32933 | direct (N × H) |
| 147. C22×C8 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#131×C41 | 2 |
| C2×C41×#466 | 2 |
| C41×#2615 | 2 |
| C41×#1895 | 2 |
| C41×#1808 | 2 |
| #32933 | 41 |