Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
662 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C131 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ #376×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 79. #32816 | C131 | direct (N × H) |
| 80. C131 | #32816 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2642×C131 | 2 |
| #2056×C131 | 2 |
| #2026×C131 | 2 |
| #2016×C131 | 2 |
| #1832×C131 | 2 |
| #32816 | 131 |