Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
1116 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C47 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#3548 | C2 | semidirect |
| 2. C47×#3151 | C2 | semidirect |
| 3. C47×#3138 | C2 | semidirect |
| 4. C47×#1656 | C2 | semidirect |
| 5. C47×#1526 | C2 | semidirect |
| 6. C47×#1525 | C2 | semidirect |
| 8. C47×#562 | C22 | semidirect |
| 25. C47×#330 | C22 | semidirect |
| 26. C47×#329 | C22 | semidirect |
| 135. #19075 | C47 | direct (N × H) |
| 151. #3548 | C2×C47 | semidirect |
| 152. #3151 | C2×C47 | semidirect |
| 153. #3138 | C2×C47 | semidirect |
| 154. #1656 | C2×C47 | semidirect |
| 155. #1526 | C2×C47 | semidirect |
| 156. #1525 | C2×C47 | semidirect |
| 163. #562 | C22×C47 | semidirect |
| 180. #330 | C22×C47 | semidirect |
| 181. #329 | C22×C47 | semidirect |
| 182. C47 | #19075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#3548 | 2 |
| C47×#3151 | 2 |
| C47×#3138 | 2 |
| C47×#1656 | 2 |
| C47×#1526 | 2 |
| C47×#1525 | 2 |
| #19075 | 47 |