Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C3×#493 | C2 | semidirect |
| 2. C2×#826 | C2 | semidirect |
| 3. #4695 | C2 | semidirect |
| 4. C4×C3⋊C16 | C2 | semidirect |
| 17. #493 | D3 | semidirect |
| 30. C3⋊C16 | D4 | semidirect |
| 69. C3×C4 | D16 | semidirect |
| 93. C4 | #826 | semidirect |
| 96. C3 | #2246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#493 | 2 |
| C2×#826 | 2 |
| #4695 | 2 |
| C4×C3⋊C16 | 2 |
| #2246 | 3 |