Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
206 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C47 | C2×D4 |
| commutator | C2×C4 | C22×C8×C47 |
| Frattini, cosocle | C4×C8 | C23×C47 |
| socle, prime radical | C22×C47 | C8×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C47 ◁ C4×C16×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 45. C16×C47 | Q16 | semidirect |
| 60. #12054 | C47 | direct (N × H) |
| 87. C47 | #12054 | direct (N × H) |
| 117. C16 | Q16×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#2183 | 2 |
| C8×Q16×C47 | 2 |
| C47×#1370 | 2 |
| C47×Q8⋊C16 | 2 |
| C8×C16×C47 | 2 |
| #12054 | 47 |