Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 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 |
|---|---|---|
| 3. #22553063 | C2 | semidirect |
| 4. #22553061 | C2 | semidirect |
| 5. #500×C131 | C2 | semidirect |
| 58. C131 | #1695 | semidirect |
| 60. #500 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553599 | 2 |
| #22553391 | 2 |
| #22553063 | 2 |
| #22553061 | 2 |
| #500×C131 | 2 |
| #1695 | 131 |