Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C3×C4×#41 | C2 | semidirect |
| 2. C2×#951 | C2 | semidirect |
| 4. C2×#875 | C2 | semidirect |
| 5. #5028 | C2 | semidirect |
| 6. #5016 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 8. #5001 | C2 | semidirect |
| 9. #4924 | C2 | semidirect |
| 14. C3×C4×Q8 | C22 | semidirect |
| 16. C3×C4×D4 | C22 | semidirect |
| 23. C2×#216 | C22 | semidirect |
| 25. C2×#214 | C22 | semidirect |
| 33. #810 | C22 | semidirect |
| 35. C4⋊(C3⋊C8) | C22 | semidirect |
| 39. C4×#41 | D3 | semidirect |
| 97. C4×Q8 | C2×D3 | semidirect |
| 99. C4×D4 | 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 |
|---|---|
| C3×C4×#41 | 2 |
| C2×#951 | 2 |
| C2×#949 | 2 |
| C2×#875 | 2 |
| #5028 | 2 |
| #5016 | 2 |
| #5004 | 2 |
| #5001 | 2 |
| #4924 | 2 |
| #3040 | 3 |