Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C3×#107 | C2 | semidirect |
| 4. #4972 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 23. #821 | C4 | semidirect |
| 26. C2×#107 | D3 | semidirect |
| 50. C2×C3×C8 | C2×C4 | semidirect |
| 57. C4⋊Dic3 | C2×C4 | semidirect |
| 112. D12 | C4⋊C4 | semidirect |
| 137. C2×C8 | C4×D3 | semidirect |
| 238. C3 | #1862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×C3×#107 | 2 |
| C2×#821 | 2 |
| #4972 | 2 |
| C2×#809 | 2 |
| #4550 | 2 |
| #4529 | 2 |
| #1862 | 3 |