Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 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×#106 | C4 | semidirect |
| 15. #817 | C4 | semidirect |
| 16. C8×Dic3 | C4 | semidirect |
| 47. #106 | Dic3 | direct (N × H) |
| 67. C3×C8 | C42 | semidirect |
| 99. Dic3 | #106 | direct (N × H) |
| 118. C8 | C4×Dic3 | semidirect |
| 137. C3 | C4×#106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#106 | 2 |
| C2×#817 | 2 |
| C2×C8×Dic3 | 2 |
| Dic3×C4⋊C4 | 2 |
| #4529 | 2 |
| C4×#106 | 3 |