Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
620 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 620 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 |
|---|---|---|
| 2. C2×#837 | C2 | semidirect |
| 3. #5232 | C2 | semidirect |
| 4. #5221 | C2 | semidirect |
| 5. C2×#833 | C2 | semidirect |
| 9. C3×H(5,𝔽2) | C4 | semidirect |
| 16. C2×C4⋊Dic3 | C22 | semidirect |
| 17. C2×C4×Dic3 | C22 | semidirect |
| 18. C2×#208 | C22 | semidirect |
| 61. H(5,𝔽2) | Dic3 | semidirect |
| 86. C3×Q8 | C22⋊C4 | semidirect |
| 93. C3×D4 | C22⋊C4 | semidirect |
| 169. Q8 | #217 | semidirect |
| 176. D4 | #217 | semidirect |
| 217. C3 | #1792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×H(5,𝔽2) | 2 |
| C2×#837 | 2 |
| #5232 | 2 |
| #5221 | 2 |
| C2×#833 | 2 |
| #1792 | 3 |