Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 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. #22553038 | C2 | semidirect |
| 52. C2×C4×C131 | M16 | semidirect |
| 75. C131 | #1463 | semidirect |
| 127. C2×C4 | #14523497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553276 | 2 |
| #22553038 | 2 |
| C22×C4⋊C4×C131 | 2 |
| #1463 | 131 |