Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#1007 | C2 | semidirect |
| 2. C2×#942 | C2 | semidirect |
| 3. C2×#904 | C2 | semidirect |
| 4. #5510 | C2 | semidirect |
| 5. C2×C3×#103 | C2 | semidirect |
| 6. #5110 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 8. #4810 | C2 | semidirect |
| 9. #4809 | C2 | semidirect |
| 10. #4808 | C2 | semidirect |
| 11. #4806 | C2 | semidirect |
| 55. C2×#103 | D3 | semidirect |
| 59. C2×C3×Q8 | D4 | semidirect |
| 79. #235 | D4 | semidirect |
| 205. C2×Q8 | D12 | semidirect |
| 331. C3 | #3013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007 | 2 |
| C2×#942 | 2 |
| C2×#904 | 2 |
| #5510 | 2 |
| C2×C3×#103 | 2 |
| #5110 | 2 |
| #4966 | 2 |
| #4810 | 2 |
| #4809 | 2 |
| #4808 | 2 |
| #4806 | 2 |
| #3013 | 3 |