Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
806 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C47 |
| prime radical | C47×#3192 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#2436 | C2 | semidirect |
| 3. C47×#1784 | C2 | semidirect |
| 4. C47×#1507 | C2 | semidirect |
| 5. C47×#1297 | C2 | semidirect |
| 122. #10327 | C47 | direct (N × H) |
| 141. #2436 | C2×C47 | semidirect |
| 142. #1784 | C2×C47 | semidirect |
| 143. #1507 | C2×C47 | semidirect |
| 144. #1297 | C2×C47 | semidirect |
| 164. C47 | #10327 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3192 | 2 |
| C47×#2436 | 2 |
| C47×#1784 | 2 |
| C47×#1507 | 2 |
| C47×#1297 | 2 |
| #10327 | 47 |