Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
1038 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #379 |
| commutator | C22×C4 | C22×C4×C41 |
| Frattini, cosocle | C23×C4 | C23×C41 |
| prime radical | C41×#3486 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#1784 | C2 | semidirect |
| 3. C41×#1504 | C2 | semidirect |
| 4. C41×#1446 | C2 | semidirect |
| 5. C2×2−1+4×C41 | C4 | semidirect |
| 10. C41×#536 | C4 | semidirect |
| 13. C41×#519 | C4 | semidirect |
| 142. #8455 | C41 | direct (N × H) |
| 163. #1784 | C2×C41 | semidirect |
| 164. #1504 | C2×C41 | semidirect |
| 165. #1446 | C2×C41 | semidirect |
| 172. C2×2−1+4 | C4×C41 | semidirect |
| 177. #536 | C4×C41 | semidirect |
| 180. #519 | C4×C41 | semidirect |
| 187. C41 | #8455 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3486 | 2 |
| C41×#1784 | 2 |
| C41×#1504 | 2 |
| C41×#1446 | 2 |
| #8455 | 41 |