Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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. C3×#443 | C2 | semidirect |
| 2. #5193 | C2 | semidirect |
| 3. #4695 | C2 | semidirect |
| 4. #4495 | C2 | semidirect |
| 5. #4463 | C2 | semidirect |
| 20. #443 | D3 | semidirect |
| 26. C3×Q16 | D4 | semidirect |
| 28. C3×D8 | D4 | semidirect |
| 69. Q16 | D12 | semidirect |
| 75. D8 | D12 | semidirect |
| 118. C3 | #2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#443 | 2 |
| #5193 | 2 |
| #4695 | 2 |
| #4495 | 2 |
| #4463 | 2 |
| #2213 | 3 |