Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
848 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 157 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×#832 | C2 | semidirect |
| 3. #5212 | C2 | semidirect |
| 4. C2×#830 | C2 | semidirect |
| 10. C22×C3×D4 | C4 | semidirect |
| 14. C2×C4⋊Dic3 | C22 | semidirect |
| 15. C22×C3⋊C8 | C22 | semidirect |
| 52. C22×D4 | Dic3 | semidirect |
| 80. C3×D4 | C22⋊C4 | semidirect |
| 127. C22×C3 | #102 | semidirect |
| 156. D4 | #217 | semidirect |
| 185. C22 | #832 | semidirect |
| 195. C3 | #1786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C2×#832 | 2 |
| #5212 | 2 |
| C2×#830 | 2 |
| #1786 | 3 |