Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
418 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C41 | #120 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C2×C42 | C23×C41 |
| socle | C22×C41 | #385 |
| prime radical | C22×D4×C41 | Q8 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C41×#1573 | C2 | semidirect |
| 5. C41×#1302 | C2 | semidirect |
| 121. #8864 | C41 | direct (N × H) |
| 146. #1573 | C2×C41 | semidirect |
| 148. #1302 | C2×C41 | semidirect |
| 171. C41 | #8864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#2973 | 2 |
| C41×#1955 | 2 |
| C41×#1573 | 2 |
| C41×#1460 | 2 |
| C41×#1302 | 2 |
| #8864 | 41 |