Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 1. #22554019 | C2 | semidirect |
| 2. #22553685 | C2 | semidirect |
| 3. #22553513 | C2 | semidirect |
| 5. #22553060 | C2 | semidirect |
| 6. #22553044 | C2 | semidirect |
| 7. D4⋊C8×C131 | C2 | semidirect |
| 66. D4×C131 | SD16 | semidirect |
| 96. C131 | #1622 | semidirect |
| 104. D4⋊C8 | D131 | semidirect |
| 158. D4 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554019 | 2 |
| #22553685 | 2 |
| #22553513 | 2 |
| #22553507 | 2 |
| #22553060 | 2 |
| #22553044 | 2 |
| D4⋊C8×C131 | 2 |
| #1622 | 131 |