Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1112 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1112 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 |
|---|---|---|
| 2. C22×#217 | C2 | semidirect |
| 3. C2×#834 | C2 | direct (N × H) |
| 5. C25×C3 | C4 | semidirect |
| 9. C22×C3×D4 | C4 | semidirect |
| 11. C23×C3×C4 | C4 | semidirect |
| 14. C2×#217 | C22 | semidirect |
| 15. #834 | C22 | direct (N × H) |
| 25. C24×C3 | C2×C4 | semidirect |
| 33. C2×C3×D4 | C2×C4 | semidirect |
| 37. C22×C3×C4 | C2×C4 | semidirect |
| 41. #217 | C23 | semidirect |
| 42. C25 | Dic3 | semidirect |
| 46. C22×D4 | Dic3 | semidirect |
| 49. C23×C4 | Dic3 | semidirect |
| 69. C23×C3 | C22×C4 | semidirect |
| 77. C2×C3×C4 | C22×C4 | semidirect |
| 86. C24 | C2×Dic3 | semidirect |
| 94. C2×D4 | C2×Dic3 | semidirect |
| 100. C22×C4 | C2×Dic3 | semidirect |
| 115. C22×C3 | #99 | semidirect |
| 139. C23 | C22×Dic3 | semidirect |
| 149. C2×C4 | C22×Dic3 | semidirect |
| 155. C2×C3 | C2×#99 | semidirect |
| 169. C22 | #834 | direct (N × H) |
| 177. C3 | C22×#99 | semidirect |
| 183. C2 | C2×#834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×D4 | 2 |
| C22×#217 | 2 |
| C2×#834 | 2 |
| C22×#99 | 3 |