Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1546 conjugacy classes of subgroups; only the 446 normal subgroups are shown.
This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 446 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 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C47 |
| Frattini, cosocle | C24 | C24×C47 |
| prime radical | C23×D4×C47 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C23×D4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C47×#1819 | C2 | semidirect |
| 4. C47×#1740 | C2 | semidirect |
| 7. C2×C4×D4×C47 | C4 | semidirect |
| 76. #20690 | C47 | direct (N × H) |
| 92. #1819 | C2×C47 | semidirect |
| 93. #1740 | C2×C47 | semidirect |
| 101. C2×C4×D4 | C4×C47 | semidirect |
| 108. C47 | #20690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C47×#518 | 2 |
| C47×#2309 | 2 |
| C47×#1819 | 2 |
| C47×#1740 | 2 |
| #20690 | 47 |