Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
194 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 78. C3×Q8 | Q16 | semidirect |
| 135. Q8 | #216 | semidirect |
| 163. C3 | #1648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5078 | 2 |
| #5031 | 2 |
| #5020 | 2 |
| #4547 | 2 |
| #4535 | 2 |
| #1648 | 3 |