Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
720 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 166 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 | #99 |
| commutator | C2×C4 | C2×C42×C47 |
| Frattini, cosocle | C22×D4 | C23×C47 |
| socle | C22×C47 | C2×#99 |
| prime radical | C2×#127×C47 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C22×C4×C47 ◁ C2×C4×D4×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×#99×C47 | C2 | semidirect |
| 4. C47×#1393 | C2 | semidirect |
| 7. C2×C4×D4×C47 | C4 | semidirect |
| 11. C47×#390 | C4 | semidirect |
| 13. C47×#384 | C4 | semidirect |
| 15. C43×C47 | C4 | semidirect |
| 16. C47×#353 | C4 | direct (N × H) |
| 45. #99×C47 | C2×C4 | semidirect |
| 57. C2×D4×C47 | C42 | semidirect |
| 90. C42×C47 | C42 | semidirect |
| 133. C4×#353 | C47 | direct (N × H) |
| 158. C4×C47 | #353 | direct (N × H) |
| 161. C4×#99 | C2×C47 | semidirect |
| 162. #1393 | C2×C47 | semidirect |
| 172. C2×C4×D4 | C4×C47 | semidirect |
| 176. #390 | C4×C47 | semidirect |
| 178. #384 | C4×C47 | semidirect |
| 180. C43 | C4×C47 | semidirect |
| 181. #353 | C4×C47 | direct (N × H) |
| 183. C47 | C4×#353 | direct (N × H) |
| 211. #99 | C2×C4×C47 | semidirect |
| 223. C2×D4 | C42×C47 | semidirect |
| 256. C42 | C42×C47 | semidirect |
| 323. C4 | C47×#353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#127×C47 | 2 |
| C2×C47×#353 | 2 |
| C4×#99×C47 | 2 |
| C47×#1393 | 2 |
| C4×#353 | 47 |