Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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×#125 | C2 | semidirect |
| 2. #5688 | C2 | direct (N × H) |
| 5. C2×#888 | C2 | semidirect |
| 6. C2×#887 | C2 | semidirect |
| 8. C2×#870 | C2 | semidirect |
| 13. C3×#125 | C22 | semidirect |
| 26. #888 | C22 | semidirect |
| 27. #887 | C22 | semidirect |
| 29. #870 | C22 | semidirect |
| 33. C2×#125 | D3 | semidirect |
| 46. C2×C4×D3 | Q8 | semidirect |
| 66. #125 | C2×D3 | semidirect |
| 98. C4×D3 | C2×Q8 | semidirect |
| 154. C2×C3 | #533 | semidirect |
| 170. C3 | C2×#533 | semidirect |
| 172. C2 | #5688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#125 | 2 |
| #5688 | 2 |
| C2×#896 | 2 |
| C2×#892 | 2 |
| C2×#888 | 2 |
| C2×#887 | 2 |
| C2×C42×D3 | 2 |
| C2×#870 | 2 |
| C2×#533 | 3 |