Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 1. C2×Q8×Dic3 | C2 | semidirect |
| 4. C2×C3×#103 | C2 | semidirect |
| 6. C2×C8×Dic3 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4788 | C2 | direct (N × H) |
| 16. Q8×Dic3 | C22 | semidirect |
| 17. C2×#215 | C4 | semidirect |
| 27. C3×#103 | C22 | semidirect |
| 29. C8×Dic3 | C22 | semidirect |
| 30. #808 | C22 | semidirect |
| 36. C2×#103 | D3 | semidirect |
| 42. C2×C3×Q8 | C2×C4 | semidirect |
| 60. #215 | C2×C4 | semidirect |
| 68. C2×C3⋊C8 | C2×C4 | semidirect |
| 88. #103 | C2×D3 | semidirect |
| 98. C3×Q8 | C22×C4 | semidirect |
| 110. C2×Dic3 | SD16 | semidirect |
| 118. C3⋊C8 | C22×C4 | semidirect |
| 122. C2×Q8 | C4×D3 | semidirect |
| 165. Dic3 | C2×SD16 | semidirect |
| 173. Q8 | C2×C4×D3 | semidirect |
| 194. C2×C3 | C4×SD16 | semidirect |
| 215. C3 | C2×C4×SD16 | semidirect |
| 217. C2 | #4788 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| C22×#215 | 2 |
| C2×#893 | 2 |
| C2×C3×#103 | 2 |
| C2×#821 | 2 |
| C2×C8×Dic3 | 2 |
| C2×#808 | 2 |
| #4788 | 2 |
| C2×C4×SD16 | 3 |