Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
308 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 17. C4×Dic6 | C4 | semidirect |
| 88. Dic6 | C4⋊C4 | semidirect |
| 123. C3×C4 | #103 | semidirect |
| 176. C4 | #816 | semidirect |
| 181. C3 | #1803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic6 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#816 | 2 |
| #4935 | 2 |
| #4551 | 2 |
| #1803 | 3 |