Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
146 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 71. C131 | #1700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553662 | 2 |
| #22553594 | 2 |
| #22553523 | 2 |
| #22553439 | 2 |
| #22553064 | 2 |
| #22553057 | 2 |
| #332×C131 | 2 |
| #1700 | 131 |