Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
192 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 87 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. D4×C131⋊C8 | C2 | semidirect |
| 2. #22553063 | C2 | semidirect |
| 3. D4⋊(C131⋊C8) | C2 | semidirect |
| 4. #22553033 | C2 | semidirect |
| 22. D8×C131 | C8 | semidirect |
| 33. D4×C131 | C2×C8 | semidirect |
| 41. C8×C131 | C2×C8 | semidirect |
| 55. C131 | #1580 | semidirect |
| 74. D8 | C131⋊C8 | semidirect |
| 86. D4 | C2×C131⋊C8 | semidirect |
| 97. C8 | C2×C131⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C131⋊C8 | 2 |
| #22553063 | 2 |
| D4⋊(C131⋊C8) | 2 |
| #22553033 | 2 |
| C4×D8×C131 | 2 |
| #1580 | 131 |