Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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×C8×D4 | C2 | semidirect |
| 3. #5007 | C2 | semidirect |
| 4. #4693 | C2 | semidirect |
| 5. #4485 | C2 | semidirect |
| 6. #4482 | C2 | semidirect |
| 7. #4457 | C2 | semidirect |
| 27. C8×D4 | D3 | semidirect |
| 69. C3×D4 | SD16 | semidirect |
| 86. C3×C8 | D8 | semidirect |
| 133. D4 | #204 | semidirect |
| 145. C8 | #213 | semidirect |
| 165. C3 | #1665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D4 | 2 |
| #5015 | 2 |
| #5007 | 2 |
| #4693 | 2 |
| #4485 | 2 |
| #4482 | 2 |
| #4457 | 2 |
| #1665 | 3 |