Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 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×#815 | C2 | semidirect |
| 5. C2×C8×Dic3 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 12. C2×C3×M16 | C4 | semidirect |
| 21. #830 | C4 | semidirect |
| 63. C2×M16 | Dic3 | semidirect |
| 99. C2×Dic3 | M16 | semidirect |
| 101. C3×C8 | C22⋊C4 | semidirect |
| 178. C8 | #217 | semidirect |
| 202. C3 | #1753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| C4×#217 | 2 |
| C2×#830 | 2 |
| C2×#815 | 2 |
| C2×C8×Dic3 | 2 |
| #4550 | 2 |
| #1753 | 3 |