Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
760 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C131 | B(4,𝔽2) |
| commutator | C2×Q8 | C22×C4×C131 |
| Frattini, cosocle | C2×#41 | C23×C131 |
| socle | C2×C131 | #1790 |
| prime radical | #3529×C131 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2126×C131 | C2 | semidirect |
| 3. #1884×C131 | C2 | semidirect |
| 4. #568×C131 | C22 | semidirect |
| 5. #563×C131 | C4 | semidirect |
| 7. H(3,𝔽4)×C131 | C4 | semidirect |
| 13. #410×C131 | C22 | semidirect |
| 126. #12772 | C131 | direct (N × H) |
| 127. C131 | #12772 | direct (N × H) |
| 129. #2126 | C2×C131 | semidirect |
| 130. #1884 | C2×C131 | semidirect |
| 131. #568 | C22×C131 | semidirect |
| 132. #563 | C4×C131 | semidirect |
| 134. H(3,𝔽4) | C4×C131 | semidirect |
| 140. #410 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3529×C131 | 2 |
| #2126×C131 | 2 |
| #1884×C131 | 2 |
| #12772 | 131 |