Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #22553364 | C2 | semidirect |
| 3. C4×C8×D131 | C2 | semidirect |
| 4. #22553044 | C2 | semidirect |
| 5. #22553042 | C2 | semidirect |
| 6. D4⋊(C131⋊C8) | C2 | semidirect |
| 7. D4⋊C8×C131 | C2 | semidirect |
| 28. #14523512 | C8 | semidirect |
| 59. Dic262 | C2×C8 | semidirect |
| 77. D4×C131 | C2×C8 | semidirect |
| 109. C131 | #1476 | semidirect |
| 117. D4⋊C8 | D131 | semidirect |
| 173. D4 | C8×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523512 | 2 |
| #22553364 | 2 |
| C4×C8×D131 | 2 |
| #22553044 | 2 |
| #22553042 | 2 |
| D4⋊(C131⋊C8) | 2 |
| D4⋊C8×C131 | 2 |
| #1476 | 131 |