Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
348 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2127 |
| commutator | C42 | C22×C4×C47 |
| Frattini, cosocle | #127 | C23×C47 |
| prime radical | C47×#3220 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C22×C47 ◁ C22×C4×C47 ◁ C47×#535 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C47×#2128 | C2 | semidirect |
| 3. C47×#2127 | C2 | semidirect |
| 4. C47×#1412 | C2 | semidirect |
| 5. C47×#1408 | C2 | semidirect |
| 6. C47×#540 | C4 | semidirect |
| 8. C47×#496 | C4 | semidirect |
| 11. C47×#488 | C4 | semidirect |
| 16. C47×#433 | C4 | semidirect |
| 29. #127×C47 | C2×C4 | semidirect |
| 32. #125×C47 | C2×C4 | semidirect |
| 54. #97×C47 | C2×C4 | semidirect |
| 55. C4×C8×C47 | C2×C4 | semidirect |
| 130. #13609 | C47 | direct (N × H) |
| 154. #2128 | C2×C47 | semidirect |
| 155. #2127 | C2×C47 | semidirect |
| 156. #1412 | C2×C47 | semidirect |
| 157. #1408 | C2×C47 | semidirect |
| 165. #540 | C4×C47 | semidirect |
| 167. #496 | C4×C47 | semidirect |
| 170. #488 | C4×C47 | semidirect |
| 175. #433 | C4×C47 | semidirect |
| 182. C47 | #13609 | direct (N × H) |
| 189. #127 | C2×C4×C47 | semidirect |
| 192. #125 | C2×C4×C47 | semidirect |
| 214. #97 | C2×C4×C47 | semidirect |
| 215. C4×C8 | C2×C4×C47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3220 | 2 |
| C47×#2128 | 2 |
| C47×#2127 | 2 |
| C47×#1412 | 2 |
| C47×#1408 | 2 |
| #13609 | 47 |