Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 368 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. C2×C3×#125 | C2 | semidirect |
| 3. #5067 | C2 | semidirect |
| 4. #5066 | C2 | semidirect |
| 5. #5064 | C2 | semidirect |
| 6. #4968 | C2 | semidirect |
| 7. #4967 | C2 | semidirect |
| 8. #4926 | C2 | semidirect |
| 35. C2×#125 | D3 | semidirect |
| 207. C3 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#125 | 2 |
| #5477 | 2 |
| #5067 | 2 |
| #5066 | 2 |
| #5064 | 2 |
| #4968 | 2 |
| #4967 | 2 |
| #4926 | 2 |
| #3234 | 3 |