Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
128 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D47 |
| commutator, cosocle | C32×C47 | C23 |
| Frattini | C32 | C22×D47 |
| Fitting | C47×SD128 | C2 |
| socle | C2×C47 | C2×D32 |
| hypercenter | SD128 | D47 |
| hypocenter | C47 | #13741 |
| LCS | G ▷ C32×C47 ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ SD128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20245698 | C2 | semidirect |
| 2. #20245694 | C2 | semidirect |
| 3. #20241605 | C2 | semidirect |
| 4. #20241604 | C2 | semidirect |
| 5. #20241600 | C2 | semidirect |
| 6. C64×D47 | C2 | semidirect |
| 7. C47×SD128 | C2 | semidirect |
| 64. SD128 | D47 | semidirect |
| 82. C47 | #13741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245698 | 2 |
| #20245694 | 2 |
| #20241605 | 2 |
| #20241604 | 2 |
| #20241600 | 2 |
| C64×D47 | 2 |
| C47×SD128 | 2 |
| #13741 | 47 |