Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
504 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #386 |
| commutator | C42 | C22×C4×C47 |
| Frattini, cosocle | C2×C42 | C23×C47 |
| prime radical | C47×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C47×#1549 | C2 | semidirect |
| 5. C47×#1299 | C2 | semidirect |
| 110. #9435 | C47 | direct (N × H) |
| 127. #1549 | C2×C47 | semidirect |
| 128. #1299 | C2×C47 | semidirect |
| 149. C47 | #9435 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3152 | 2 |
| C47×#2979 | 2 |
| C47×#1560 | 2 |
| C47×#1549 | 2 |
| C47×#1299 | 2 |
| #9435 | 47 |