Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
144 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C47 | C2×D4 |
| commutator | C4 | C22×C8×C47 |
| Frattini, cosocle | C2×C8 | C23×C47 |
| socle | C2×C47 | C8×D4 |
| prime radical | #135×C47 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C47 ◁ C2×C16×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#504 | C2 | semidirect |
| 3. C47×#364 | C2 | semidirect |
| 4. C47×#350 | C2 | semidirect |
| 5. C47×#346 | C2 | semidirect |
| 46. #2171 | C47 | direct (N × H) |
| 50. #504 | C2×C47 | semidirect |
| 52. #364 | C2×C47 | semidirect |
| 53. #350 | C2×C47 | semidirect |
| 54. #346 | C2×C47 | semidirect |
| 55. C47 | #2171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#504 | 2 |
| C47×#443 | 2 |
| C47×#364 | 2 |
| C47×#350 | 2 |
| C47×#346 | 2 |
| #2171 | 47 |