Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
300 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 21. #888 | C4 | semidirect |
| 42. C2×C3×C8 | Q8 | semidirect |
| 58. C2×C3⋊C8 | Q8 | semidirect |
| 116. C2×C8 | Dic6 | semidirect |
| 199. C3 | #1990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#888 | 2 |
| C2×C8×Dic3 | 2 |
| #4975 | 2 |
| C3×#340 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| #1990 | 3 |