Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
432 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C131⋊#401 | C2 | semidirect |
| 2. #22553253 | C2 | semidirect |
| 5. C4×Dic131⋊C4 | C2 | semidirect |
| 7. #376×C131 | C2 | semidirect |
| 70. C131 | #2401 | semidirect |
| 78. #376 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C131⋊#401 | 2 |
| #22553253 | 2 |
| #22553241 | 2 |
| #22553236 | 2 |
| C4×Dic131⋊C4 | 2 |
| C4×(C2×D131)⋊C4 | 2 |
| #376×C131 | 2 |
| #2401 | 131 |