Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
478 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C2×AΣL(1,𝔽16) |
| commutator | C2×D4 | C22×C4×C131 |
| Frattini, cosocle | #124 | C23×C131 |
| prime radical | #3018×C131 | C2 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #532×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2132×C131 | C2 | semidirect |
| 3. #1536×C131 | C2 | semidirect |
| 4. #1403×C131 | C2 | semidirect |
| 17. #355×C131 | C22 | semidirect |
| 19. #329×C131 | C22 | semidirect |
| 172. #13566 | C131 | direct (N × H) |
| 173. C131 | #13566 | direct (N × H) |
| 175. #2132 | C2×C131 | semidirect |
| 176. #1536 | C2×C131 | semidirect |
| 177. #1403 | C2×C131 | semidirect |
| 190. #355 | C22×C131 | semidirect |
| 192. #329 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3018×C131 | 2 |
| #2132×C131 | 2 |
| #1536×C131 | 2 |
| #1403×C131 | 2 |
| #13566 | 131 |