Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
432 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 217 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. Q8×C131⋊C8 | C2 | semidirect |
| 3. C8×D524 | C2 | semidirect |
| 4. #22553377 | C2 | semidirect |
| 5. #22553363 | C2 | semidirect |
| 6. C4⋊C8×D131 | C2 | semidirect |
| 7. C8×Q8×C131 | C2 | semidirect |
| 24. #14523514 | C8 | semidirect |
| 43. D524 | C2×C8 | semidirect |
| 50. C4×D131 | C2×C8 | semidirect |
| 53. Q8×C131 | C2×C8 | semidirect |
| 74. C131 | #2988 | semidirect |
| 78. C8×Q8 | D131 | semidirect |
| 118. 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 |
| Q8×C131⋊C8 | 2 |
| C8×D524 | 2 |
| #22553377 | 2 |
| #22553363 | 2 |
| C4⋊C8×D131 | 2 |
| C8×Q8×C131 | 2 |
| #2988 | 131 |