Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
330 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C2×C22⋊C4 |
| commutator | C23 | C22×C8×C47 |
| Frattini, cosocle | C22×C8 | C23×C47 |
| socle | C22×C47 | C2×C22⋊C8 |
| prime radical | C23×C47 | C22×C8 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C2×C4×C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 71. #11494 | C47 | direct (N × H) |
| 100. C47 | #11494 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×Q8×C47 | 2 |
| C47×#2163 | 2 |
| C47×#1322 | 2 |
| #11494 | 47 |