Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #5225 | C2 | semidirect |
| 5. #4523 | C2 | semidirect |
| 10. C3×#124 | C4 | semidirect |
| 28. C2×C3×Q8 | C2×C4 | semidirect |
| 39. C3×C42 | C2×C4 | semidirect |
| 51. #124 | Dic3 | semidirect |
| 84. C2×Q8 | C2×Dic3 | semidirect |
| 102. C42 | C2×Dic3 | semidirect |
| 155. C3 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#124 | 2 |
| #5798 | 2 |
| #5225 | 2 |
| C2×#833 | 2 |
| #4523 | 2 |
| #1885 | 3 |