Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
782 conjugacy classes of subgroups.
The subgroup lattice has 132 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C47 | D8 |
| commutator | C8 | C23×C4×C47 |
| Frattini, cosocle | C2×C8 | C24×C47 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C47 ◁ C23×C4×C47 ◁ C23×C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C47×#366 | C2 | direct (N × H) |
| 6. C22×C16×C47 | C4 | semidirect |
| 10. C47×#366 | C22 | direct (N × H) |
| 19. C2×C16×C47 | C2×C4 | semidirect |
| 37. C16×C47 | C22×C4 | semidirect |
| 52. C22×#366 | C47 | direct (N × H) |
| 53. C22×C47 | #366 | direct (N × H) |
| 64. C2×#366 | C2×C47 | direct (N × H) |
| 65. C2×C47 | C2×#366 | direct (N × H) |
| 71. C22×C16 | C4×C47 | semidirect |
| 75. #366 | C22×C47 | direct (N × H) |
| 76. C47 | C22×#366 | direct (N × H) |
| 85. C2×C16 | C2×C4×C47 | semidirect |
| 103. C16 | C22×C4×C47 | semidirect |
| 118. C22 | C47×#366 | direct (N × H) |
| 127. C2 | C2×C47×#366 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C16×C47 | 2 |
| C22×#107×C47 | 2 |
| C2×C47×#366 | 2 |
| C22×#366 | 47 |