Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 81 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. C3×C4×M16 | C2 | semidirect |
| 3. #4926 | C2 | semidirect |
| 4. #4459 | C2 | semidirect |
| 17. C3×C4×C8 | C22 | semidirect |
| 19. C4⋊(C3⋊C8) | C22 | semidirect |
| 23. C4×M16 | D3 | semidirect |
| 61. C4×C8 | C2×D3 | semidirect |
| 80. D12 | M16 | semidirect |
| 165. C3 | #1490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×C4×M16 | 2 |
| #4926 | 2 |
| #4459 | 2 |
| #1490 | 3 |