Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 40. #216 | C8 | direct (N × H) |
| 76. C3×C8 | Q16 | semidirect |
| 125. C8 | #216 | direct (N × H) |
| 139. C3 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| C4×#216 | 2 |
| C8×Dic6 | 2 |
| #4535 | 2 |
| #4484 | 2 |
| #4479 | 2 |
| C8×C3⋊C8 | 2 |
| C8×Q16 | 3 |