Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
350 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 180 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 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C24×C41 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ #41×C41 ◁ #131×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C41×#578 | C2 | semidirect |
| 2. C41×#510 | C2 | semidirect |
| 3. C41×#508 | C2 | semidirect |
| 4. C2×Q32×C41 | C2 | semidirect |
| 5. C41×#504 | C2 | semidirect |
| 46. #3417 | C41 | direct (N × H) |
| 50. #578 | C2×C41 | semidirect |
| 51. #510 | C2×C41 | semidirect |
| 52. #508 | C2×C41 | semidirect |
| 53. C2×Q32 | C2×C41 | semidirect |
| 54. #504 | C2×C41 | semidirect |
| 55. C41 | #3417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#578 | 2 |
| C41×#510 | 2 |
| C41×#508 | 2 |
| C2×Q32×C41 | 2 |
| C41×#504 | 2 |
| #3417 | 41 |