Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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. #22553710 | C2 | semidirect |
| 3. #22553135 | C2 | semidirect |
| 5. #364×C131 | C2 | semidirect |
| 17. Dic524 | Q8 | semidirect |
| 19. D1048 | Q8 | semidirect |
| 52. C131 | #2230 | semidirect |
| 57. #364 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553710 | 2 |
| #22553430 | 2 |
| #22553135 | 2 |
| #22553123 | 2 |
| #364×C131 | 2 |
| #2230 | 131 |