Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. #5805 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. C2×#901 | C2 | semidirect |
| 4. #5510 | C2 | semidirect |
| 5. C2×C3×#102 | C2 | semidirect |
| 6. #5113 | C2 | semidirect |
| 7. #4964 | C2 | semidirect |
| 8. #4782 | C2 | semidirect |
| 9. #4780 | C2 | semidirect |
| 10. #4778 | C2 | semidirect |
| 11. #4775 | C2 | semidirect |
| 30. C2×ΓL(1,𝔽25) | C22 | semidirect |
| 31. C2×D3×C8 | C22 | semidirect |
| 33. #897 | C22 | semidirect |
| 35. #895 | C22 | semidirect |
| 38. #821 | C22 | semidirect |
| 39. #821 | C22 | semidirect |
| 40. #816 | C22 | semidirect |
| 41. #816 | C22 | semidirect |
| 42. #808 | C22 | semidirect |
| 43. #807 | C22 | semidirect |
| 54. C2×#102 | D3 | semidirect |
| 93. #208 | D4 | semidirect |
| 295. C3 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5805 | 2 |
| C2×#932 | 2 |
| C2×#901 | 2 |
| #5510 | 2 |
| C2×C3×#102 | 2 |
| #5113 | 2 |
| #4964 | 2 |
| #4782 | 2 |
| #4780 | 2 |
| #4778 | 2 |
| #4775 | 2 |
| #3062 | 3 |