Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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×#533 | C2 | semidirect |
| 3. #5089 | C2 | semidirect |
| 4. #5086 | C2 | semidirect |
| 5. #5050 | C2 | semidirect |
| 7. #5028 | C2 | semidirect |
| 8. #4926 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 13. C3×C4⋊Q8 | C22 | semidirect |
| 18. C3×C4×Q8 | C22 | semidirect |
| 21. C2×#216 | C22 | semidirect |
| 30. #810 | C22 | semidirect |
| 32. C4⋊(C3⋊C8) | C22 | semidirect |
| 33. #803 | C22 | semidirect |
| 34. #533 | D3 | semidirect |
| 78. C4⋊Q8 | C2×D3 | semidirect |
| 79. C4⋊Q8 | C2×D3 | semidirect |
| 88. C4×Q8 | C2×D3 | semidirect |
| 219. C3 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| C2×#875 | 2 |
| #5089 | 2 |
| #5086 | 2 |
| #5050 | 2 |
| #5046 | 2 |
| #5028 | 2 |
| #4926 | 2 |
| #3215 | 3 |