Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 2. #22553598 | C2 | semidirect |
| 4. #22553442 | C2 | semidirect |
| 5. #22553057 | C2 | semidirect |
| 7. #335×C131 | C2 | semidirect |
| 62. C8×C131 | SD16 | semidirect |
| 79. C131 | #1686 | semidirect |
| 85. #335 | D131 | semidirect |
| 142. C8 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553685 | 2 |
| #22553598 | 2 |
| #22553513 | 2 |
| #22553442 | 2 |
| #22553057 | 2 |
| #22553055 | 2 |
| #335×C131 | 2 |
| #1686 | 131 |