Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5521 | C2 | semidirect |
| 3. #5139 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #5005 | C2 | semidirect |
| 6. C3×H(3,ℤ/4) | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 20. #875 | C4 | semidirect |
| 21. #874 | C4 | semidirect |
| 32. H(3,ℤ/4) | D3 | semidirect |
| 46. C2×D12 | C2×C4 | semidirect |
| 50. C2×Dic6 | C2×C4 | semidirect |
| 58. C3×C42 | C2×C4 | semidirect |
| 59. C3×C42 | D4 | semidirect |
| 64. C4×Dic3 | D4 | semidirect |
| 150. C42 | C4×D3 | semidirect |
| 151. C42 | D12 | semidirect |
| 226. C3 | #1911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5525 | 2 |
| #5521 | 2 |
| #5139 | 2 |
| C2×#823 | 2 |
| #5005 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4531 | 2 |
| #1911 | 3 |