Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. C2×#822 | C2 | semidirect |
| 5. #4998 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. #4559 | C2 | semidirect |
| 18. #907 | C4 | semidirect |
| 19. #907 | C4 | semidirect |
| 34. #344 | D3 | semidirect |
| 205. C3 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#907 | 2 |
| #5139 | 2 |
| C2×#822 | 2 |
| #5005 | 2 |
| #4998 | 2 |
| C3×#344 | 2 |
| #4559 | 2 |
| #1814 | 3 |