Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22553659 | C2 | semidirect |
| 2. #22553603 | C2 | semidirect |
| 4. #22553391 | C2 | semidirect |
| 5. #22553060 | C2 | semidirect |
| 6. #22553055 | C2 | semidirect |
| 7. #335×C131 | C2 | semidirect |
| 82. C131 | #1697 | semidirect |
| 88. #335 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553659 | 2 |
| #22553603 | 2 |
| #22553508 | 2 |
| #22553391 | 2 |
| #22553060 | 2 |
| #22553055 | 2 |
| #335×C131 | 2 |
| #1697 | 131 |