Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
280 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C47 | #410 |
| commutator | C22×C4 | C22×C4×C47 |
| Frattini, cosocle | C2×M16 | C23×C47 |
| socle | C2×C47 | #1464 |
| prime radical | C2×#41×C47 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C47 ◁ C42×C47 ◁ C4×M16×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#2165 | C2 | semidirect |
| 3. C47×#1328 | C2 | semidirect |
| 86. #11523 | C47 | direct (N × H) |
| 100. #2165 | C2×C47 | semidirect |
| 101. #1328 | C2×C47 | semidirect |
| 119. C47 | #11523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2923 | 2 |
| C47×#2165 | 2 |
| C47×#1328 | 2 |
| C47×#1321 | 2 |
| #11523 | 47 |