Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22553710 | C2 | semidirect |
| 5. #22553060 | C2 | semidirect |
| 6. #22553059 | C2 | semidirect |
| 7. #335×C131 | C2 | semidirect |
| 59. C8×C131 | SD16 | semidirect |
| 76. C131 | #1691 | semidirect |
| 82. #335 | D131 | semidirect |
| 136. C8 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553710 | 2 |
| #22553603 | 2 |
| #22553518 | 2 |
| #22553391 | 2 |
| #22553060 | 2 |
| #22553059 | 2 |
| #335×C131 | 2 |
| #1691 | 131 |