Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
294 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C41 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C2×C4×C41 ◁ C22×C8×C41 ◁ C2×M32×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#3414 | C2 | semidirect |
| 2. C41×#2263 | C2 | semidirect |
| 3. C41×#2218 | C2 | semidirect |
| 4. C41×#1418 | C2 | semidirect |
| 5. C41×#1400 | C2 | semidirect |
| 11. C2×D16×C41 | C22 | semidirect |
| 16. C41×M64 | C22 | semidirect |
| 17. C41×#367 | C22 | semidirect |
| 31. Q32×C41 | D4 | semidirect |
| 36. D16×C41 | D4 | semidirect |
| 93. #13667 | C41 | direct (N × H) |
| 107. #3414 | C2×C41 | semidirect |
| 108. #2263 | C2×C41 | semidirect |
| 109. #2218 | C2×C41 | semidirect |
| 110. #1418 | C2×C41 | semidirect |
| 111. #1400 | C2×C41 | semidirect |
| 122. C2×D16 | C22×C41 | semidirect |
| 127. M64 | C22×C41 | semidirect |
| 128. #367 | C22×C41 | semidirect |
| 130. C41 | #13667 | direct (N × H) |
| 143. Q32 | D4×C41 | semidirect |
| 148. D16 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3414 | 2 |
| C41×#2263 | 2 |
| C41×#2218 | 2 |
| C41×#1418 | 2 |
| C41×#1400 | 2 |
| #13667 | 41 |