Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 13. C3×#97 | C4 | semidirect |
| 14. #815 | C4 | semidirect |
| 15. C8×Dic3 | C4 | semidirect |
| 16. #803 | C4 | semidirect |
| 45. #97 | Dic3 | direct (N × H) |
| 58. C3×C8 | C42 | semidirect |
| 59. C3⋊C8 | C42 | semidirect |
| 83. Dic3 | #97 | direct (N × H) |
| 96. C8 | C4×Dic3 | semidirect |
| 110. C3 | C4×#97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#97 | 2 |
| C2×#815 | 2 |
| C2×C8×Dic3 | 2 |
| C42×Dic3 | 2 |
| C2×#803 | 2 |
| C4×#97 | 3 |