Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
276 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 276 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. #22553336 | C2 | semidirect |
| 3. #22553041 | C2 | semidirect |
| 4. C2×C4×C8×C131 | C2 | semidirect |
| 85. C131 | #1492 | semidirect |
| 89. C2×C4×C8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553862 | 2 |
| #22553336 | 2 |
| #22553041 | 2 |
| C2×C4×C8×C131 | 2 |
| #1492 | 131 |