Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. #22553133 | C2 | semidirect |
| 4. #22553132 | C2 | semidirect |
| 5. #364×C131 | C2 | semidirect |
| 63. D131 | #364 | direct (N × H) |
| 64. C131 | C2×#364 | semidirect |
| 70. #364 | D131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D131 | 2 |
| C4×C8×D131 | 2 |
| #22553133 | 2 |
| #22553132 | 2 |
| #364×C131 | 2 |
| C2×#364 | 131 |