Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22553712 | C2 | semidirect |
| 3. #22553135 | C2 | semidirect |
| 4. #22553134 | C2 | semidirect |
| 5. #22553132 | C2 | semidirect |
| 59. C131 | #2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553712 | 2 |
| #22553429 | 2 |
| #22553135 | 2 |
| #22553134 | 2 |
| #22553132 | 2 |
| #22553122 | 2 |
| #360×C131 | 2 |
| #2231 | 131 |