Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C3×#137 | C2 | semidirect |
| 2. Dic3×#41 | C2 | semidirect |
| 4. C2×#947 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5185 | C2 | semidirect |
| 7. #5165 | C2 | semidirect |
| 8. #5131 | C2 | semidirect |
| 9. #5118 | C2 | semidirect |
| 15. C2×C3×Q16 | C22 | semidirect |
| 16. C2×C3×SD16 | C22 | semidirect |
| 22. Q8×Dic3 | C22 | semidirect |
| 25. D4×Dic3 | C22 | semidirect |
| 33. #835 | C22 | semidirect |
| 35. Dic3⋊C8 | C22 | semidirect |
| 36. C2×#137 | D3 | semidirect |
| 88. C2×Q16 | C2×D3 | semidirect |
| 90. C2×SD16 | C2×D3 | semidirect |
| 245. C3 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| Dic3×#41 | 2 |
| C2×#949 | 2 |
| C2×#947 | 2 |
| #5225 | 2 |
| #5185 | 2 |
| #5165 | 2 |
| #5131 | 2 |
| #5118 | 2 |
| #3040 | 3 |