Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22553363 | C2 | semidirect |
| 3. C4⋊C8×D131 | C2 | semidirect |
| 4. Q8⋊(C131⋊C8) | C2 | semidirect |
| 5. #22553041 | C2 | semidirect |
| 6. #22553039 | C2 | semidirect |
| 7. Q8⋊C8×C131 | C2 | semidirect |
| 28. #14523514 | C8 | semidirect |
| 61. D524 | C2×C8 | semidirect |
| 78. Q8×C131 | C2×C8 | semidirect |
| 109. C131 | #1477 | semidirect |
| 115. Q8⋊C8 | D131 | semidirect |
| 170. Q8 | C8×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523514 | 2 |
| #22553363 | 2 |
| C4⋊C8×D131 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553041 | 2 |
| #22553039 | 2 |
| Q8⋊C8×C131 | 2 |
| #1477 | 131 |