Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5518 | C2 | semidirect |
| 3. #5239 | C2 | semidirect |
| 4. #5218 | C2 | semidirect |
| 5. #5076 | C2 | semidirect |
| 6. #5075 | C2 | semidirect |
| 7. #5071 | C2 | semidirect |
| 8. #5060 | C2 | semidirect |
| 9. #5056 | C2 | semidirect |
| 10. #5054 | C2 | semidirect |
| 11. #5000 | C2 | semidirect |
| 22. C2×#216 | C22 | semidirect |
| 25. C2×#214 | C22 | semidirect |
| 29. #870 | C22 | semidirect |
| 30. #869 | C22 | semidirect |
| 31. C4×Dic6 | C22 | semidirect |
| 32. #835 | C22 | semidirect |
| 35. #832 | C22 | semidirect |
| 37. C4⋊(C3⋊C8) | C22 | semidirect |
| 38. #803 | C22 | semidirect |
| 39. C4×C3⋊C8 | C22 | semidirect |
| 238. C3 | #3222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5518 | 2 |
| #5239 | 2 |
| #5218 | 2 |
| #5076 | 2 |
| #5075 | 2 |
| #5071 | 2 |
| #5060 | 2 |
| #5056 | 2 |
| #5054 | 2 |
| #5000 | 2 |
| #3222 | 3 |