Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
182 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 69 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. #4688 | C2 | semidirect |
| 4. D4⋊(C3⋊C8) | C2 | semidirect |
| 5. #4483 | C2 | semidirect |
| 6. #4479 | C2 | semidirect |
| 7. #4455 | C2 | semidirect |
| 26. C8×D4 | D3 | semidirect |
| 68. C3×D4 | M16 | semidirect |
| 82. C3×C8 | D8 | semidirect |
| 125. D4 | ΓL(1,𝔽25) | semidirect |
| 141. C8 | #213 | semidirect |
| 161. C3 | #1581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D4 | 2 |
| C4×#213 | 2 |
| #4688 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4483 | 2 |
| #4479 | 2 |
| #4455 | 2 |
| #1581 | 3 |