Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22554078 | C2 | semidirect |
| 3. #22553294 | C2 | semidirect |
| 4. #22553276 | C2 | semidirect |
| 5. #22553084 | C2 | semidirect |
| 6. #22553083 | C2 | semidirect |
| 7. #407×C131 | C2 | semidirect |
| 42. C2×C131⋊C8 | D4 | semidirect |
| 64. C2×C8×C131 | D4 | semidirect |
| 125. C131 | #1891 | semidirect |
| 131. #407 | D131 | semidirect |
| 184. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554078 | 2 |
| #22553823 | 2 |
| #22553294 | 2 |
| #22553276 | 2 |
| #22553084 | 2 |
| #22553083 | 2 |
| #407×C131 | 2 |
| #1891 | 131 |