Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#127 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. #5477 | C2 | semidirect |
| 4. #5076 | C2 | semidirect |
| 5. #5074 | C2 | semidirect |
| 6. #5073 | C2 | semidirect |
| 7. C4×#208 | C2 | semidirect |
| 16. C2×#214 | C22 | semidirect |
| 18. C2×#213 | C22 | semidirect |
| 21. #875 | C22 | semidirect |
| 22. #874 | C22 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. #803 | C22 | semidirect |
| 26. C4×C3⋊C8 | C22 | semidirect |
| 29. C2×#127 | D3 | semidirect |
| 56. #208 | D4 | semidirect |
| 97. C3⋊C8 | C2×D4 | semidirect |
| 132. C3×C4 | AGL(1,ℤ/8) | semidirect |
| 172. C4 | #932 | semidirect |
| 175. C3 | #3151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| C2×#932 | 2 |
| #5477 | 2 |
| #5076 | 2 |
| #5074 | 2 |
| #5073 | 2 |
| C4×#208 | 2 |
| #3151 | 3 |