Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
186 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 30 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×C47 | #1408 |
| commutator | C4×C8 | C2×C4×C47 |
| Frattini, cosocle | #493 | C22×C47 |
| prime radical | C47×#1712 | C2 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C22×C47 ◁ C2×C4×C47 ◁ C42×C47 ◁ C47×#493 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#1408 | C2 | semidirect |
| 4. C47×#493 | C4 | semidirect |
| 7. C82×C47 | C4 | semidirect |
| 38. #7529 | C47 | direct (N × H) |
| 48. #1408 | C2×C47 | semidirect |
| 54. #493 | C4×C47 | semidirect |
| 57. C82 | C4×C47 | semidirect |
| 58. C47 | #7529 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#1712 | 2 |
| C47×#1408 | 2 |
| #7529 | 47 |