Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 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×#541 | C2 | semidirect |
| 3. #5083 | C2 | semidirect |
| 4. #5066 | C2 | semidirect |
| 6. #5045 | C2 | semidirect |
| 7. #5026 | C2 | semidirect |
| 8. C4×#215 | C2 | semidirect |
| 9. #5000 | C2 | semidirect |
| 12. C3×C4⋊Q8 | C22 | semidirect |
| 15. C3×#125 | C22 | semidirect |
| 17. C3×C4×Q8 | C22 | semidirect |
| 26. #835 | C22 | semidirect |
| 27. #835 | C22 | semidirect |
| 31. #808 | C22 | semidirect |
| 32. #807 | C22 | semidirect |
| 33. C4⋊(C3⋊C8) | C22 | semidirect |
| 34. #803 | C22 | semidirect |
| 35. C4×C3⋊C8 | C22 | semidirect |
| 36. #541 | D3 | semidirect |
| 76. C4⋊Q8 | C2×D3 | semidirect |
| 79. #125 | C2×D3 | semidirect |
| 81. C4×Q8 | C2×D3 | semidirect |
| 200. C3 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#541 | 2 |
| #5521 | 2 |
| #5083 | 2 |
| #5066 | 2 |
| #5046 | 2 |
| #5045 | 2 |
| #5026 | 2 |
| C4×#215 | 2 |
| #5000 | 2 |
| #3123 | 3 |