Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#915 | C2 | semidirect |
| 2. #5727 | C2 | semidirect |
| 4. C3×#461 | C2 | semidirect |
| 5. #5173 | C2 | semidirect |
| 6. #5092 | C2 | semidirect |
| 7. C4×#214 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4838 | C2 | semidirect |
| 10. #4816 | C2 | semidirect |
| 11. #4809 | C2 | semidirect |
| 49. #461 | D3 | semidirect |
| 78. #214 | D4 | semidirect |
| 204. C3×C4 | #137 | semidirect |
| 260. C4 | #915 | semidirect |
| 263. C3 | #3276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#915 | 2 |
| #5727 | 2 |
| #5555 | 2 |
| C3×#461 | 2 |
| #5173 | 2 |
| #5092 | 2 |
| C4×#214 | 2 |
| #4849 | 2 |
| #4838 | 2 |
| #4816 | 2 |
| #4809 | 2 |
| #3276 | 3 |