Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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×C4⋊C4 | C2 | semidirect |
| 3. #4990 | C2 | semidirect |
| 4. #4989 | C2 | semidirect |
| 5. #4940 | C2 | semidirect |
| 6. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 7. #4937 | C2 | semidirect |
| 9. #4646 | C2 | semidirect |
| 25. #875 | C4 | semidirect |
| 40. C4×C4⋊C4 | D3 | semidirect |
| 57. C2×Dic6 | C2×C4 | semidirect |
| 61. C3×C42 | C2×C4 | semidirect |
| 65. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 66. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 150. C42 | C4×D3 | semidirect |
| 230. C3 | #2337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C3×C4×C4⋊C4 | 2 |
| #4990 | 2 |
| #4989 | 2 |
| #4940 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4937 | 2 |
| #4665 | 2 |
| #4646 | 2 |
| #2337 | 3 |