Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #353 |
| commutator | C42 | C2×C8×C131 |
| Frattini, cosocle | #384 | C22×C131 |
| prime radical | C23×C131 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #384×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C4⋊Q8×C131 | C8 | semidirect |
| 73. #7355 | C131 | direct (N × H) |
| 74. C131 | #7355 | direct (N × H) |
| 86. C4⋊Q8 | C8×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1956×C131 | 2 |
| #1325×C131 | 2 |
| #7355 | 131 |