Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 4. C2×#815 | C2 | semidirect |
| 5. Dic3×C4⋊C4 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 15. D4×Dic3 | C4 | semidirect |
| 21. C3×#102 | C4 | semidirect |
| 22. #832 | C4 | semidirect |
| 50. C2×C3×C8 | C2×C4 | semidirect |
| 52. C3×C4⋊C4 | C2×C4 | semidirect |
| 57. C4⋊Dic3 | C2×C4 | semidirect |
| 63. C2×C3⋊C8 | C2×C4 | semidirect |
| 77. #102 | Dic3 | semidirect |
| 91. C3×D4 | C42 | semidirect |
| 137. C2×C8 | C2×Dic3 | semidirect |
| 143. C4⋊C4 | C2×Dic3 | semidirect |
| 182. D4 | C4×Dic3 | semidirect |
| 238. C3 | #1762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#815 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| #1762 | 3 |