Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22553658 | C2 | semidirect |
| 3. #22553593 | C2 | semidirect |
| 4. #22553518 | C2 | semidirect |
| 5. #22553039 | C2 | semidirect |
| 6. #22553039 | C2 | semidirect |
| 7. #331×C131 | C2 | semidirect |
| 11. #16862246 | C22 | semidirect |
| 21. C4×C131⋊C8 | C22 | semidirect |
| 23. C4⋊C8×C131 | C22 | semidirect |
| 24. C4⋊C8×C131 | C22 | semidirect |
| 62. D524 | SD16 | semidirect |
| 109. C131 | #1639 | semidirect |
| 115. #331 | D131 | semidirect |
| 129. C4⋊C8 | C2×D131 | semidirect |
| 130. C4⋊C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553947 | 2 |
| #22553658 | 2 |
| #22553593 | 2 |
| #22553518 | 2 |
| #22553039 | 2 |
| #331×C131 | 2 |
| #1639 | 131 |