Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#946 | C2 | semidirect |
| 2. C2×#942 | C2 | semidirect |
| 3. C2×D3×M16 | C2 | semidirect |
| 5. C3×#419 | C2 | semidirect |
| 6. #5133 | C2 | semidirect |
| 7. #4995 | C2 | semidirect |
| 8. #4816 | C2 | semidirect |
| 9. #4813 | C2 | semidirect |
| 10. #4812 | C2 | semidirect |
| 11. #4807 | C2 | semidirect |
| 22. C2×#216 | C22 | semidirect |
| 24. C2×#215 | C22 | semidirect |
| 40. C3×#103 | C22 | semidirect |
| 41. C3×#103 | C22 | semidirect |
| 42. #821 | C22 | semidirect |
| 43. #816 | C22 | semidirect |
| 44. #808 | C22 | semidirect |
| 45. #807 | C22 | semidirect |
| 55. #419 | D3 | semidirect |
| 100. #208 | D4 | semidirect |
| 134. #103 | C2×D3 | semidirect |
| 135. #103 | C2×D3 | semidirect |
| 237. C2×D3 | #137 | semidirect |
| 319. C3 | #3056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#946 | 2 |
| C2×#942 | 2 |
| C2×D3×M16 | 2 |
| #5524 | 2 |
| C3×#419 | 2 |
| #5133 | 2 |
| #4995 | 2 |
| #4816 | 2 |
| #4813 | 2 |
| #4812 | 2 |
| #4807 | 2 |
| #3056 | 3 |