Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 213 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. #4682 | C2 | direct (N × H) |
| 25. C2×C3×C8 | Q8 | semidirect |
| 52. C3×C8 | C2×Q8 | semidirect |
| 59. C2×C8 | Dic6 | semidirect |
| 86. C8 | C2×Dic6 | semidirect |
| 87. C2×C3 | #500 | semidirect |
| 100. C3 | C2×#500 | semidirect |
| 101. C2 | #4682 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#869 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#818 | 2 |
| #4682 | 2 |
| C2×#500 | 3 |