Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 140 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 |
|---|---|---|
| 69. C131 | #1704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553663 | 2 |
| #22553607 | 2 |
| #22553597 | 2 |
| #22553063 | 2 |
| #22553060 | 2 |
| #22553059 | 2 |
| #446×C131 | 2 |
| #1704 | 131 |