Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#16862192 | C2 | semidirect |
| 5. #22553690 | C2 | semidirect |
| 6. #22553087 | C2 | semidirect |
| 7. C2×Q32×C131 | C2 | semidirect |
| 73. C131 | #2251 | semidirect |
| 76. C2×Q32 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862192 | 2 |
| C2×#16862191 | 2 |
| C2×#16862189 | 2 |
| #22553697 | 2 |
| #22553690 | 2 |
| #22553087 | 2 |
| C2×Q32×C131 | 2 |
| #2251 | 131 |