Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 8. #4790 | C2 | direct (N × H) |
| 16. C2×#216 | C4 | semidirect |
| 58. #216 | C2×C4 | semidirect |
| 107. C2×Dic3 | Q16 | semidirect |
| 157. Dic3 | C2×Q16 | semidirect |
| 183. C2×C3 | C4×Q16 | semidirect |
| 200. C3 | C2×C4×Q16 | semidirect |
| 201. C2 | #4790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| C22×#216 | 2 |
| C2×#887 | 2 |
| C2×C3×#103 | 2 |
| C2×#816 | 2 |
| C2×C8×Dic3 | 2 |
| C2×#807 | 2 |
| #4790 | 2 |
| C2×C4×Q16 | 3 |