Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
182 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 182 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 |
|---|---|---|
| 2. D4×C3⋊C8 | C2 | semidirect |
| 3. #4838 | C2 | semidirect |
| 4. C3×D4⋊C8 | C2 | semidirect |
| 5. #4479 | C2 | semidirect |
| 6. #4459 | C2 | semidirect |
| 7. #4454 | C2 | semidirect |
| 29. D4⋊C8 | D3 | semidirect |
| 68. C3×D4 | M16 | semidirect |
| 86. C3⋊C8 | D8 | semidirect |
| 125. D4 | ΓL(1,𝔽25) | semidirect |
| 161. C3 | #1581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#213 | 2 |
| D4×C3⋊C8 | 2 |
| #4838 | 2 |
| C3×D4⋊C8 | 2 |
| #4479 | 2 |
| #4459 | 2 |
| #4454 | 2 |
| #1581 | 3 |