Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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×#131 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #5110 | C2 | semidirect |
| 6. #4558 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 19. C2×#216 | C4 | semidirect |
| 20. C2×#215 | C4 | semidirect |
| 21. C2×#214 | C4 | semidirect |
| 22. C2×#213 | C4 | semidirect |
| 31. C2×#131 | D3 | semidirect |
| 253. C3 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C2×#950 | 2 |
| C2×#837 | 2 |
| C2×#825 | 2 |
| #5110 | 2 |
| #4558 | 2 |
| #4550 | 2 |
| #1876 | 3 |