Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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. C3×#431 | C2 | semidirect |
| 3. #4924 | C2 | semidirect |
| 4. #4459 | C2 | semidirect |
| 18. C3×C4×C8 | C22 | semidirect |
| 20. C4⋊(C3⋊C8) | C22 | semidirect |
| 22. #431 | D3 | semidirect |
| 62. C4×C8 | C2×D3 | semidirect |
| 82. D12 | M16 | semidirect |
| 173. C3 | #1486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×#431 | 2 |
| #4924 | 2 |
| #4459 | 2 |
| #1486 | 3 |