Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#888 | C2 | semidirect |
| 5. C2×#817 | C2 | semidirect |
| 6. C2×Dic3⋊C8 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4761 | C2 | direct (N × H) |
| 24. #888 | C22 | semidirect |
| 27. #817 | C22 | semidirect |
| 28. Dic3⋊C8 | C22 | semidirect |
| 29. #808 | C22 | semidirect |
| 41. C2×C3×D4 | Q8 | semidirect |
| 94. C3×D4 | C2×Q8 | semidirect |
| 118. C2×D4 | Dic6 | semidirect |
| 166. D4 | C2×Dic6 | semidirect |
| 185. C2×C3 | #476 | semidirect |
| 205. C3 | C2×#476 | semidirect |
| 207. C2 | #4761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C2×#888 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#817 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#808 | 2 |
| #4761 | 2 |
| C2×#476 | 3 |