Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
618 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 129 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. C4×#217 | C2 | semidirect |
| 4. #5207 | C2 | semidirect |
| 9. C2×C3×#41 | C4 | semidirect |
| 11. C22×C3×Q8 | C4 | semidirect |
| 13. C22×C3×D4 | C4 | semidirect |
| 17. C2×C4×Dic3 | C22 | semidirect |
| 18. C2×#208 | C22 | semidirect |
| 63. C2×#41 | Dic3 | semidirect |
| 65. C22×Q8 | Dic3 | semidirect |
| 67. C22×D4 | Dic3 | semidirect |
| 89. C3×Q8 | C22⋊C4 | semidirect |
| 94. C3×D4 | C22⋊C4 | semidirect |
| 158. C22×C3 | #104 | semidirect |
| 179. Q8 | #217 | semidirect |
| 184. D4 | #217 | semidirect |
| 222. C22 | #837 | semidirect |
| 231. C3 | #1789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41 | 2 |
| C2×#837 | 2 |
| C4×#217 | 2 |
| #5207 | 2 |
| #1789 | 3 |