Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 1. #5745 | C2 | semidirect |
| 3. #5131 | C2 | semidirect |
| 4. #5006 | C2 | semidirect |
| 5. #5001 | C2 | semidirect |
| 6. C3×H(3,ℤ/4) | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 21. #875 | C4 | semidirect |
| 22. #874 | C4 | semidirect |
| 32. H(3,ℤ/4) | D3 | semidirect |
| 52. C2×C3×C8 | D4 | semidirect |
| 65. C2×C3⋊C8 | D4 | semidirect |
| 140. C2×C8 | D12 | semidirect |
| 224. C3 | #1910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5745 | 2 |
| #5525 | 2 |
| #5131 | 2 |
| #5006 | 2 |
| #5001 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4531 | 2 |
| #1910 | 3 |