Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
238 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 42 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 | #1343 |
| commutator | C22×C8 | C2×C4×C131 |
| Frattini, cosocle | #408 | C22×C131 |
| prime radical | C2×#41×C131 | D4 |
| LCS | G ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #408×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C22×Q16×C131 | C4 | semidirect |
| 10. #341×C131 | C4 | semidirect |
| 95. #7399 | C131 | direct (N × H) |
| 96. C131 | #7399 | direct (N × H) |
| 101. C22×Q16 | C4×C131 | semidirect |
| 106. #341 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2020×C131 | 2 |
| #1391×C131 | 2 |
| #1321×C131 | 2 |
| #7399 | 131 |