Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
356 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 4. #4683 | C2 | semidirect |
| 5. #4682 | C2 | semidirect |
| 6. #4680 | C2 | semidirect |
| 29. C2×C3×C8 | Q8 | semidirect |
| 66. C2×C8 | Dic6 | semidirect |
| 107. C3 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C2×C3×C4×C8 | 2 |
| #5106 | 2 |
| #4683 | 2 |
| #4682 | 2 |
| #4680 | 2 |
| #3160 | 3 |