Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22553662 | C2 | semidirect |
| 3. #22553522 | C2 | semidirect |
| 4. #22553061 | C2 | semidirect |
| 5. Q8⋊(C131⋊C8) | C2 | semidirect |
| 59. D4×C131 | Q16 | semidirect |
| 88. C131 | #1644 | semidirect |
| 144. D4 | #14523503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553662 | 2 |
| #22553592 | 2 |
| #22553522 | 2 |
| #22553061 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| D4⋊(C131⋊C8) | 2 |
| #554×C131 | 2 |
| #1644 | 131 |