Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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×#1010 | C2 | semidirect |
| 2. C2×C3×#131 | C2 | semidirect |
| 3. #5753 | C2 | direct (N × H) |
| 4. C2×#909 | C2 | semidirect |
| 5. C22×Dic12 | C2 | semidirect |
| 6. C2×#904 | C2 | semidirect |
| 10. #1010 | C22 | semidirect |
| 15. C3×#131 | C22 | semidirect |
| 18. #909 | C22 | semidirect |
| 21. C2×Dic12 | C22 | semidirect |
| 22. #904 | C22 | semidirect |
| 30. C2×#131 | D3 | semidirect |
| 70. #131 | C2×D3 | semidirect |
| 146. C2×C3 | #578 | semidirect |
| 158. C3 | C2×#578 | semidirect |
| 161. C2 | #5753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C2×C3×#131 | 2 |
| #5753 | 2 |
| C2×#909 | 2 |
| C22×Dic12 | 2 |
| C2×#904 | 2 |
| C2×#578 | 3 |