Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C22×C3×C4⋊C4 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. #4968 | C2 | direct (N × H) |
| 5. C2×#809 | C2 | semidirect |
| 6. C2×#808 | C2 | semidirect |
| 15. C2×C3×C4⋊C4 | C22 | semidirect |
| 21. #830 | C22 | semidirect |
| 22. #809 | C22 | semidirect |
| 23. #808 | C22 | semidirect |
| 25. C22×C4⋊C4 | D3 | semidirect |
| 65. C2×C4⋊C4 | C2×D3 | semidirect |
| 162. C2×C3 | #481 | semidirect |
| 184. C3 | C2×#481 | semidirect |
| 187. C2 | #4968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C2×#930 | 2 |
| C2×#830 | 2 |
| #4968 | 2 |
| C2×#809 | 2 |
| C2×#808 | 2 |
| C2×#481 | 3 |