Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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. C2×C3×#131 | C2 | semidirect |
| 3. #5827 | C2 | semidirect |
| 4. #5133 | C2 | semidirect |
| 5. #5131 | C2 | semidirect |
| 6. #5113 | C2 | semidirect |
| 7. C2×#821 | C2 | semidirect |
| 11. #1009 | C4 | semidirect |
| 17. C2×C3×M16 | C22 | semidirect |
| 18. C22×C3×C8 | C22 | semidirect |
| 21. #926 | C22 | semidirect |
| 22. C2×C4⋊Dic3 | C22 | semidirect |
| 23. #821 | C22 | semidirect |
| 24. #821 | C22 | semidirect |
| 25. #821 | C22 | semidirect |
| 26. #816 | C22 | semidirect |
| 27. #816 | C22 | semidirect |
| 29. C2×#131 | D3 | semidirect |
| 46. #235 | C2×C4 | semidirect |
| 49. C2×D12 | C2×C4 | semidirect |
| 70. C2×M16 | C2×D3 | semidirect |
| 71. C22×C8 | C2×D3 | semidirect |
| 189. C3 | #2897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C2×C3×#131 | 2 |
| #5827 | 2 |
| #5133 | 2 |
| #5131 | 2 |
| #5113 | 2 |
| C2×#821 | 2 |
| #2897 | 3 |