Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
470 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1351×C131 | C2 | semidirect |
| 5. #1344×C131 | C2 | semidirect |
| 6. C2×C4×Q8×C131 | C4 | semidirect |
| 11. #397×C131 | C4 | semidirect |
| 14. #393×C131 | C4 | semidirect |
| 19. #376×C131 | C4 | semidirect |
| 178. #11728 | C131 | direct (N × H) |
| 179. C131 | #11728 | direct (N × H) |
| 183. #1351 | C2×C131 | semidirect |
| 184. #1344 | C2×C131 | semidirect |
| 185. C2×C4×Q8 | C4×C131 | semidirect |
| 190. #397 | C4×C131 | semidirect |
| 193. #393 | C4×C131 | semidirect |
| 198. #376 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2398×C131 | 2 |
| C4×#99×C131 | 2 |
| #1459×C131 | 2 |
| #1351×C131 | 2 |
| #1344×C131 | 2 |
| #11728 | 131 |