Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
452 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 217 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. #5207 | C2 | semidirect |
| 3. #5012 | C2 | semidirect |
| 4. #4925 | C2 | semidirect |
| 13. C2×#208 | C22 | semidirect |
| 15. #830 | C22 | semidirect |
| 16. C4⋊(C3⋊C8) | C22 | semidirect |
| 17. C4×C3⋊C8 | C22 | semidirect |
| 61. C2×C3×C4 | M16 | semidirect |
| 108. C2×C4 | #208 | semidirect |
| 133. C3 | #2975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| #5207 | 2 |
| #5012 | 2 |
| #4925 | 2 |
| #2975 | 3 |