Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22553377 | C2 | semidirect |
| 3. #22553039 | C2 | semidirect |
| 4. #22553033 | C2 | semidirect |
| 5. #334×C131 | C2 | semidirect |
| 18. D1048 | C8 | semidirect |
| 30. D524 | C2×C8 | semidirect |
| 41. C8×C131 | C2×C8 | semidirect |
| 55. C131 | #1580 | semidirect |
| 59. #334 | D131 | semidirect |
| 97. C8 | C8×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1048 | 2 |
| #22553377 | 2 |
| #22553039 | 2 |
| #22553033 | 2 |
| #334×C131 | 2 |
| #1580 | 131 |