Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
256 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | #2206×C131 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ C82×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2226×C131 | C2 | semidirect |
| 3. #1706×C131 | C2 | semidirect |
| 4. C8×D8×C131 | C2 | semidirect |
| 5. #1367×C131 | C2 | semidirect |
| 6. #1365×C131 | C2 | semidirect |
| 7. #1361×C131 | C2 | semidirect |
| 56. D8×C131 | SD16 | semidirect |
| 114. #12418 | C131 | direct (N × H) |
| 115. C131 | #12418 | direct (N × H) |
| 116. #2226 | C2×C131 | semidirect |
| 118. #1706 | C2×C131 | semidirect |
| 119. C8×D8 | C2×C131 | semidirect |
| 120. #1367 | C2×C131 | semidirect |
| 121. #1365 | C2×C131 | semidirect |
| 122. #1361 | C2×C131 | semidirect |
| 171. D8 | SD16×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2226×C131 | 2 |
| #2206×C131 | 2 |
| #1706×C131 | 2 |
| C8×D8×C131 | 2 |
| #1367×C131 | 2 |
| #1365×C131 | 2 |
| #1361×C131 | 2 |
| #12418 | 131 |