Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #4837 | C2 | semidirect |
| 3. #4833 | C2 | semidirect |
| 4. C3×#331 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. #4485 | C2 | semidirect |
| 7. #4485 | C2 | semidirect |
| 19. C3×C4⋊C8 | C22 | semidirect |
| 20. C3×C4⋊C8 | C22 | semidirect |
| 24. C4⋊(C3⋊C8) | C22 | semidirect |
| 25. C4⋊(C3⋊C8) | C22 | semidirect |
| 32. #331 | D3 | semidirect |
| 73. C4⋊C8 | C2×D3 | semidirect |
| 74. C4⋊C8 | C2×D3 | semidirect |
| 216. C3 | #1545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#127 | 2 |
| #4837 | 2 |
| #4833 | 2 |
| C3×#331 | 2 |
| #4544 | 2 |
| #4485 | 2 |
| #1545 | 3 |