Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 376 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. C22×#208 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. C4×#217 | C2 | semidirect |
| 5. #4532 | C2 | semidirect |
| 10. C3×C22⋊Q8 | C4 | semidirect |
| 11. C3×C22⋊Q8 | C4 | semidirect |
| 12. C3×#121 | C4 | semidirect |
| 13. C3×#121 | C4 | semidirect |
| 64. #208 | D4 | semidirect |
| 74. C22⋊Q8 | Dic3 | semidirect |
| 75. C22⋊Q8 | Dic3 | semidirect |
| 76. #121 | Dic3 | semidirect |
| 77. #121 | Dic3 | semidirect |
| 167. C22×C3 | #104 | semidirect |
| 231. C22 | #837 | semidirect |
| 243. C3 | #1871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#525 | 2 |
| C22×#208 | 2 |
| C2×#837 | 2 |
| C4×#217 | 2 |
| #4532 | 2 |
| #1871 | 3 |