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 |
|---|---|---|
| 3. C2×#887 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. C2×C8×Dic3 | C2 | semidirect |
| 7. C2×#808 | C2 | semidirect |
| 8. #4758 | C2 | direct (N × H) |
| 18. C2×#214 | C4 | semidirect |
| 26. #887 | C22 | semidirect |
| 28. #816 | C22 | semidirect |
| 29. C8×Dic3 | C22 | semidirect |
| 30. #808 | C22 | semidirect |
| 54. C2×Dic6 | C2×C4 | semidirect |
| 61. #214 | C2×C4 | semidirect |
| 68. C2×C3⋊C8 | C2×C4 | semidirect |
| 111. C2×Dic3 | SD16 | semidirect |
| 116. Dic6 | C22×C4 | semidirect |
| 118. C3⋊C8 | C22×C4 | semidirect |
| 165. Dic3 | C2×SD16 | semidirect |
| 195. C2×C3 | C4×SD16 | semidirect |
| 215. C3 | C2×C4×SD16 | semidirect |
| 217. C2 | #4758 | 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 |
| C22×#214 | 2 |
| C2×#887 | 2 |
| C2×C3×#102 | 2 |
| C2×#816 | 2 |
| C2×C8×Dic3 | 2 |
| C2×#808 | 2 |
| #4758 | 2 |
| C2×C4×SD16 | 3 |