Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
262 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 57. C3×C16 | Q16 | semidirect |
| 58. C3⋊C16 | Q16 | semidirect |
| 96. C16 | #216 | semidirect |
| 125. C3 | #12521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2252 | 2 |
| #71384 | 2 |
| #71362 | 2 |
| #69044 | 2 |
| C16×C3⋊C8 | 2 |
| #12521 | 3 |