Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
182 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 182 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 | C2×C131 | #2177 |
| commutator | C16 | C22×C4×C131 |
| Frattini, cosocle | C2×C16 | C23×C131 |
| prime radical | #508×C131 | C22 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C4×C8×C131 ◁ #346×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2176×C131 | C2 | semidirect |
| 4. #1426×C131 | C2 | semidirect |
| 5. #1420×C131 | C2 | semidirect |
| 7. #1398×C131 | C2 | semidirect |
| 12. Q64×C131 | C4 | semidirect |
| 13. SD64×C131 | C4 | semidirect |
| 83. #13657 | C131 | direct (N × H) |
| 84. C131 | #13657 | direct (N × H) |
| 87. #2176 | C2×C131 | semidirect |
| 88. #1426 | C2×C131 | semidirect |
| 89. #1420 | C2×C131 | semidirect |
| 91. #1398 | C2×C131 | semidirect |
| 96. Q64 | C4×C131 | semidirect |
| 97. SD64 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2264×C131 | 2 |
| #2179×C131 | 2 |
| #2176×C131 | 2 |
| #1426×C131 | 2 |
| #1420×C131 | 2 |
| #1418×C131 | 2 |
| #1398×C131 | 2 |
| #13657 | 131 |