Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×C8 | C2 | semidirect |
| 4. #5102 | C2 | semidirect |
| 6. #4552 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 17. #821 | C4 | semidirect |
| 19. #816 | C4 | semidirect |
| 26. C2×C4×C8 | D3 | semidirect |
| 175. C3 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C8 | 2 |
| #5113 | 2 |
| #5110 | 2 |
| #5102 | 2 |
| C2×#805 | 2 |
| #4552 | 2 |
| #4523 | 2 |
| #1937 | 3 |