Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 53 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. #22553599 | C2 | semidirect |
| 3. C8×D524 | C2 | semidirect |
| 4. #22553063 | C2 | semidirect |
| 5. #22553061 | C2 | semidirect |
| 6. #22553056 | C2 | semidirect |
| 7. #486×C131 | C2 | semidirect |
| 82. C131 | #1677 | semidirect |
| 84. #486 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553599 | 2 |
| #22553504 | 2 |
| C8×D524 | 2 |
| #22553063 | 2 |
| #22553061 | 2 |
| #22553056 | 2 |
| #486×C131 | 2 |
| #1677 | 131 |