Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#16862178 | C2 | semidirect |
| 4. #22553080 | C2 | semidirect |
| 5. C2×#108×C131 | C2 | semidirect |
| 8. #16862252 | C4 | semidirect |
| 84. C131 | #1815 | semidirect |
| 87. C2×#108 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862252 | 2 |
| C2×#16862178 | 2 |
| #22553314 | 2 |
| #22553080 | 2 |
| C2×#108×C131 | 2 |
| #1815 | 131 |