Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. #4694 | C2 | semidirect |
| 3. #4693 | C2 | semidirect |
| 4. #4682 | C2 | semidirect |
| 5. C3×C82 | C2 | semidirect |
| 20. C82 | D3 | semidirect |
| 52. C3×C8 | D8 | semidirect |
| 53. C3×C8 | SD16 | semidirect |
| 84. C8 | #204 | semidirect |
| 85. C8 | D24 | semidirect |
| 98. C3 | #1706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4695 | 2 |
| #4694 | 2 |
| #4693 | 2 |
| #4682 | 2 |
| C3×C82 | 2 |
| #1706 | 3 |