Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
3598 conjugacy classes of subgroups.
The subgroup lattice has 156 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C47 | C24 |
| commutator | C2 | C23×C42×C47 |
| Frattini, cosocle | C23 | C25×C47 |
| socle | C23×C47 | C25 |
| prime radical | C22×#41×C47 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#2276 | C2 | semidirect |
| 3. C47×#2275 | C2 | semidirect |
| 4. C4×#117×C47 | C2 | semidirect |
| 5. C2×C47×#376 | C2 | semidirect |
| 7. C4×#41×C47 | C4 | semidirect |
| 24. C4×Q8×C47 | C2×C4 | semidirect |
| 25. C4×D4×C47 | C2×C4 | semidirect |
| 26. #117×C47 | C2×C4 | semidirect |
| 29. C2×C42×C47 | C2×C4 | semidirect |
| 37. #41×C47 | C42 | semidirect |
| 66. #33999 | C47 | direct (N × H) |
| 76. #2276 | C2×C47 | semidirect |
| 77. #2275 | C2×C47 | semidirect |
| 78. C4×#117 | C2×C47 | semidirect |
| 79. C2×#376 | C2×C47 | semidirect |
| 84. C4×#41 | C4×C47 | semidirect |
| 96. C47 | #33999 | direct (N × H) |
| 102. C4×Q8 | C2×C4×C47 | semidirect |
| 103. C4×D4 | C2×C4×C47 | semidirect |
| 104. #117 | C2×C4×C47 | semidirect |
| 107. C2×C42 | C2×C4×C47 | semidirect |
| 115. #41 | C42×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#41×C47 | 2 |
| C47×#2276 | 2 |
| C47×#2275 | 2 |
| C4×#117×C47 | 2 |
| C2×C47×#376 | 2 |
| #33999 | 47 |