Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
384 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #386 |
| commutator | C42 | C22×C4×C131 |
| Frattini, cosocle | C2×C42 | C23×C131 |
| prime radical | C23×C131 | #123 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 132. #9420 | C131 | direct (N × H) |
| 133. C131 | #9420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3165×C131 | 2 |
| #2987×C131 | 2 |
| #1558×C131 | 2 |
| #1556×C131 | 2 |
| #1537×C131 | 2 |
| #1291×C131 | 2 |
| #9420 | 131 |