Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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. #5816 | C2 | semidirect |
| 2. C22×#215 | C2 | semidirect |
| 4. #5521 | C2 | semidirect |
| 5. C3×#419 | C2 | semidirect |
| 6. #5119 | C2 | semidirect |
| 7. #5002 | C2 | semidirect |
| 8. #4819 | C2 | semidirect |
| 9. #4818 | C2 | semidirect |
| 16. #947 | C22 | semidirect |
| 18. #944 | C22 | semidirect |
| 30. C3×#103 | C22 | semidirect |
| 31. Dic3⋊C8 | C22 | semidirect |
| 32. #810 | C22 | semidirect |
| 33. #809 | C22 | semidirect |
| 41. #419 | D3 | semidirect |
| 98. #103 | C2×D3 | semidirect |
| 227. C3 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5816 | 2 |
| C22×#215 | 2 |
| C2×#908 | 2 |
| #5521 | 2 |
| C3×#419 | 2 |
| #5119 | 2 |
| #5002 | 2 |
| #4819 | 2 |
| #4818 | 2 |
| #3042 | 3 |