Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1598 conjugacy classes of subgroups.
The subgroup lattice has 350 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C47 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C47 |
| prime radical | C24×C47 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C47×#2612 | C2 | semidirect |
| 5. C47×#2606 | C2 | semidirect |
| 6. C47×#2605 | C2 | semidirect |
| 59. C2×C42×C47 | Q8 | semidirect |
| 150. #35120 | C47 | direct (N × H) |
| 172. #2612 | C2×C47 | semidirect |
| 173. #2606 | C2×C47 | semidirect |
| 174. #2605 | C2×C47 | semidirect |
| 216. C47 | #35120 | direct (N × H) |
| 234. C2×C42 | Q8×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2855 | 2 |
| C47×#2659 | 2 |
| C47×#2646 | 2 |
| C47×#2612 | 2 |
| C47×#2606 | 2 |
| C47×#2605 | 2 |
| C47×#2329 | 2 |
| C47×#2283 | 2 |
| C2×C47×#376 | 2 |
| #35120 | 47 |