Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
470 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | C2×AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C47 |
| Frattini, cosocle | C4⋊Q8 | C23×C47 |
| prime radical | C2×2−1+4×C47 | C4 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C23×C47 ◁ C22×C4×C47 ◁ C2×C4⋊Q8×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C47×#356 | C2 | semidirect |
| 3. C47×#1558 | C2 | semidirect |
| 4. C47×#1405 | C2 | semidirect |
| 17. C47×#356 | C22 | semidirect |
| 19. C47×#333 | C22 | semidirect |
| 147. #13573 | C47 | direct (N × H) |
| 164. C2×#356 | C2×C47 | semidirect |
| 165. #1558 | C2×C47 | semidirect |
| 166. #1405 | C2×C47 | semidirect |
| 184. #356 | C22×C47 | semidirect |
| 186. #333 | C22×C47 | semidirect |
| 187. C47 | #13573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C47×#456 | 2 |
| C2×C47×#356 | 2 |
| C47×#1558 | 2 |
| C47×#1405 | 2 |
| #13573 | 47 |