Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
290 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 126 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×C131 | C2×D16 |
| commutator | C16 | C22×C4×C131 |
| Frattini, cosocle | C2×C16 | C23×C131 |
| prime radical | C23×C131 | D16 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C22×C8×C131 ◁ C22×C16×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1416×C131 | C2 | semidirect |
| 8. C2×Q32×C131 | C4 | semidirect |
| 77. #13618 | C131 | direct (N × H) |
| 78. C131 | #13618 | direct (N × H) |
| 82. #1416 | C2×C131 | semidirect |
| 86. C2×Q32 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q32×C131 | 2 |
| C2×M64×C131 | 2 |
| #2158×C131 | 2 |
| #1416×C131 | 2 |
| #13618 | 131 |