Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. C2×Dic3⋊C8 | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 38. #217 | C8 | semidirect |
| 77. C2×Dic3 | C2×C8 | semidirect |
| 106. C22×C3 | C4⋊C8 | semidirect |
| 152. C22 | Dic3⋊C8 | semidirect |
| 164. C3 | #1850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊C8 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C4×#217 | 2 |
| C2×Dic3⋊C8 | 2 |
| #4550 | 2 |
| #1850 | 3 |