Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
252 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C131 |
| prime radical | #1667×C131 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C42×C131 ◁ C8×D4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2248×C131 | C2 | semidirect |
| 2. D4×C16×C131 | C2 | semidirect |
| 3. #1669×C131 | C2 | semidirect |
| 5. #1372×C131 | C2 | semidirect |
| 6. #1362×C131 | C2 | semidirect |
| 7. #1361×C131 | C2 | semidirect |
| 73. C16×C131 | D8 | semidirect |
| 84. D4×C131 | SD32 | semidirect |
| 117. #12432 | C131 | direct (N × H) |
| 118. C131 | #12432 | direct (N × H) |
| 119. #2248 | C2×C131 | semidirect |
| 120. D4×C16 | C2×C131 | semidirect |
| 121. #1669 | C2×C131 | semidirect |
| 123. #1372 | C2×C131 | semidirect |
| 124. #1362 | C2×C131 | semidirect |
| 125. #1361 | C2×C131 | semidirect |
| 191. C16 | D8×C131 | semidirect |
| 202. D4 | SD32×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2248×C131 | 2 |
| D4×C16×C131 | 2 |
| #1669×C131 | 2 |
| #1667×C131 | 2 |
| #1372×C131 | 2 |
| #1362×C131 | 2 |
| #1361×C131 | 2 |
| #12432 | 131 |