Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
600 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 4. #4984 | C2 | semidirect |
| 8. C2×C3×C4⋊C4 | C4 | semidirect |
| 39. C2×C4⋊C4 | Dic3 | semidirect |
| 52. C2×C3×C4 | C4⋊C4 | semidirect |
| 98. C2×C4 | C4⋊Dic3 | semidirect |
| 122. C3 | #2316 | semidirect |
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×#926 | 2 |
| #5212 | 2 |
| #4984 | 2 |
| #2316 | 3 |