Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
412 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #1555 |
| commutator | C42 | C22×C4×C131 |
| Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | #3151×C131 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C4×M16×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2165×C131 | C2 | semidirect |
| 3. #1359×C131 | C2 | semidirect |
| 4. #1357×C131 | C2 | semidirect |
| 14. #364×C131 | C22 | semidirect |
| 117. #11992 | C131 | direct (N × H) |
| 118. C131 | #11992 | direct (N × H) |
| 120. #2165 | C2×C131 | semidirect |
| 121. #1359 | C2×C131 | semidirect |
| 122. #1357 | C2×C131 | semidirect |
| 132. #364 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3151×C131 | 2 |
| #2165×C131 | 2 |
| #1359×C131 | 2 |
| #1357×C131 | 2 |
| #11992 | 131 |