Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
354 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C47 |
| prime radical | C23×C47 | C2×D8 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×C4⋊C8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 102. C2×C4×C47 | Q32 | semidirect |
| 107. #12162 | C47 | direct (N × H) |
| 145. C47 | #12162 | direct (N × H) |
| 229. C2×C4 | Q32×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3249 | 2 |
| C47×#2188 | 2 |
| C47×#2056 | 2 |
| C47×#1348 | 2 |
| C47×#1322 | 2 |
| #12162 | 47 |