Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
116 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 116 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 | C2×C131 | #1333 |
| commutator | C16 | C2×C8×C131 |
| Frattini, cosocle | #346 | C22×C131 |
| prime radical | C22×C131 | #361 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C4×C8×C131 ◁ #346×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 52. #7391 | C131 | direct (N × H) |
| 53. C131 | #7391 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2176×C131 | 2 |
| #1398×C131 | 2 |
| #1369×C131 | 2 |
| #7391 | 131 |