Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
816 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 309 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. #5212 | C2 | semidirect |
| 4. #4950 | C2 | semidirect |
| 9. C2×C3×C22⋊C4 | C4 | semidirect |
| 14. C2×C4⋊Dic3 | C22 | semidirect |
| 15. C3⋊#95 | C22 | semidirect |
| 27. C22×C3×C4 | C2×C4 | semidirect |
| 32. C3×C22⋊C4 | C2×C4 | semidirect |
| 43. C2×C22⋊C4 | Dic3 | semidirect |
| 51. C23×C3 | C4⋊C4 | semidirect |
| 75. C22×C4 | C2×Dic3 | semidirect |
| 80. C22⋊C4 | C2×Dic3 | semidirect |
| 101. C23 | C4⋊Dic3 | semidirect |
| 136. C3 | #2315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C22⋊C4 | 2 |
| C22×#217 | 2 |
| #5212 | 2 |
| #4950 | 2 |
| #2315 | 3 |