Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
424 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C41 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C2×M16×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3199 | C2 | semidirect |
| 2. C41×#2190 | C2 | semidirect |
| 3. C41×#2017 | C2 | semidirect |
| 4. C41×#1341 | C2 | semidirect |
| 5. C41×#1321 | C2 | semidirect |
| 7. C41×#575 | C22 | semidirect |
| 17. C41×#349 | C22 | semidirect |
| 18. C41×#338 | C22 | semidirect |
| 129. #12117 | C41 | direct (N × H) |
| 147. #3199 | C2×C41 | semidirect |
| 148. #2190 | C2×C41 | semidirect |
| 149. #2017 | C2×C41 | semidirect |
| 150. #1341 | C2×C41 | semidirect |
| 151. #1321 | C2×C41 | semidirect |
| 159. #575 | C22×C41 | semidirect |
| 169. #349 | C22×C41 | semidirect |
| 170. #338 | C22×C41 | semidirect |
| 171. C41 | #12117 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3199 | 2 |
| C41×#2190 | 2 |
| C41×#2017 | 2 |
| C41×#1341 | 2 |
| C41×#1321 | 2 |
| #12117 | 41 |