Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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. #5827 | C2 | semidirect |
| 3. C2×#948 | C2 | semidirect |
| 4. #5233 | C2 | semidirect |
| 5. #5232 | C2 | semidirect |
| 6. #5215 | C2 | semidirect |
| 7. C2×#832 | C2 | semidirect |
| 10. C3×H(5,𝔽2) | C4 | semidirect |
| 19. #926 | C22 | semidirect |
| 20. C2×C4⋊Dic3 | C22 | semidirect |
| 21. C2×#208 | C22 | semidirect |
| 22. C22×C3⋊C8 | C22 | semidirect |
| 23. #835 | C22 | semidirect |
| 24. #835 | C22 | semidirect |
| 25. #832 | C22 | semidirect |
| 26. #832 | C22 | semidirect |
| 27. #832 | C22 | semidirect |
| 39. C3×#41 | C2×C4 | semidirect |
| 47. C2×C3×D4 | C2×C4 | semidirect |
| 63. H(5,𝔽2) | Dic3 | semidirect |
| 109. #41 | C2×Dic3 | semidirect |
| 117. C2×D4 | C2×Dic3 | semidirect |
| 189. C3 | #2897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| #5827 | 2 |
| C2×#948 | 2 |
| #5233 | 2 |
| #5232 | 2 |
| #5215 | 2 |
| C2×#832 | 2 |
| #2897 | 3 |