Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
164 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 69 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×#16862186 | C2 | semidirect |
| 2. C2×C16×D131 | C2 | semidirect |
| 4. Dic131⋊C16 | C2 | semidirect |
| 5. (C2×D131)⋊C16 | C2 | semidirect |
| 6. #22553087 | C2 | semidirect |
| 7. C22⋊C16×C131 | C2 | semidirect |
| 32. C131⋊C16 | D4 | semidirect |
| 63. C2×D131 | M32 | semidirect |
| 75. C131 | #2168 | semidirect |
| 82. C22⋊C16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862186 | 2 |
| C2×C16×D131 | 2 |
| C8×C22⋊D131 | 2 |
| Dic131⋊C16 | 2 |
| (C2×D131)⋊C16 | 2 |
| #22553087 | 2 |
| C22⋊C16×C131 | 2 |
| #2168 | 131 |