Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#904 | C2 | semidirect |
| 2. #5553 | C2 | semidirect |
| 3. C3×C8×D4 | C2 | semidirect |
| 4. #5115 | C2 | semidirect |
| 5. #4848 | C2 | semidirect |
| 6. #4734 | C2 | semidirect |
| 7. C4×Dic12 | C2 | semidirect |
| 8. #4695 | C2 | semidirect |
| 37. C8×D4 | D3 | semidirect |
| 60. Dic12 | D4 | semidirect |
| 142. C3×C4 | #135 | semidirect |
| 186. C4 | #904 | semidirect |
| 189. C3 | #3287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5553 | 2 |
| C3×C8×D4 | 2 |
| #5115 | 2 |
| #4848 | 2 |
| #4734 | 2 |
| C4×Dic12 | 2 |
| #4695 | 2 |
| #3287 | 3 |