Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1088 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 341 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×#926 | C2 | semidirect |
| 4. #5212 | C2 | semidirect |
| 5. #5211 | C2 | semidirect |
| 6. C4×#217 | C2 | semidirect |
| 10. C23×C3×C4 | C4 | semidirect |
| 18. C2×C4⋊Dic3 | C22 | semidirect |
| 19. C2×C4×Dic3 | C22 | semidirect |
| 20. C3⋊#95 | C22 | semidirect |
| 51. C23×C4 | Dic3 | semidirect |
| 77. C2×C3×C4 | C22⋊C4 | semidirect |
| 114. C22×C3 | #117 | semidirect |
| 139. C2×C4 | #217 | semidirect |
| 156. C22 | #926 | semidirect |
| 165. C3 | #2280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C4 | 2 |
| C2×#926 | 2 |
| #5247 | 2 |
| #5212 | 2 |
| #5211 | 2 |
| C4×#217 | 2 |
| #2280 | 3 |