Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
198 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22553689 | C2 | semidirect |
| 2. #22553508 | C2 | semidirect |
| 3. #22553391 | C2 | semidirect |
| 4. #22553055 | C2 | semidirect |
| 5. #334×C131 | C2 | semidirect |
| 50. C8×C131 | D8 | semidirect |
| 68. C131 | #1687 | semidirect |
| 73. #334 | D131 | semidirect |
| 119. C8 | D1048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553689 | 2 |
| #22553508 | 2 |
| #22553391 | 2 |
| #22553055 | 2 |
| #334×C131 | 2 |
| #1687 | 131 |