Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic262 | C2 | semidirect |
| 4. #22553060 | C2 | semidirect |
| 5. Q8⋊(C131⋊C8) | C2 | semidirect |
| 6. #22553042 | C2 | semidirect |
| 53. Dic262 | SD16 | semidirect |
| 61. Q8×C131 | SD16 | semidirect |
| 91. C131 | #1623 | semidirect |
| 148. Q8 | #14523501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic262 | 2 |
| #22553684 | 2 |
| #22553509 | 2 |
| #22553060 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553042 | 2 |
| #460×C131 | 2 |
| #1623 | 131 |