Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
856 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 856 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, socle | C2×C131 | #1790 |
| commutator | C2×D4 | C22×C4×C131 |
| Frattini, cosocle | C2×#41 | C23×C131 |
| prime radical | #3549×C131 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×#41×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2132×C131 | C2 | semidirect |
| 3. #2122×C131 | C2 | semidirect |
| 4. #1914×C131 | C2 | semidirect |
| 5. #1884×C131 | C2 | semidirect |
| 6. #568×C131 | C22 | semidirect |
| 8. H(3,𝔽4)×C131 | C4 | semidirect |
| 12. D42×C131 | C4 | semidirect |
| 19. #413×C131 | C22 | semidirect |
| 21. #410×C131 | C22 | semidirect |
| 206. #12769 | C131 | direct (N × H) |
| 207. C131 | #12769 | direct (N × H) |
| 209. #2132 | C2×C131 | semidirect |
| 210. #2122 | C2×C131 | semidirect |
| 211. #1914 | C2×C131 | semidirect |
| 212. #1884 | C2×C131 | semidirect |
| 213. #568 | C22×C131 | semidirect |
| 215. H(3,𝔽4) | C4×C131 | semidirect |
| 219. D42 | C4×C131 | semidirect |
| 226. #413 | C22×C131 | semidirect |
| 228. #410 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3549×C131 | 2 |
| #2132×C131 | 2 |
| #2122×C131 | 2 |
| #1914×C131 | 2 |
| #1884×C131 | 2 |
| #12769 | 131 |