Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#951 | C2 | semidirect |
| 3. C2×C4×Dic6 | C2 | semidirect |
| 4. #5232 | C2 | semidirect |
| 5. #5090 | C2 | semidirect |
| 6. #5075 | C2 | semidirect |
| 7. #5054 | C2 | semidirect |
| 8. #4924 | C2 | semidirect |
| 58. C2×Dic6 | D4 | semidirect |
| 179. C3×C4 | #137 | semidirect |
| 232. C4 | #951 | semidirect |
| 235. C3 | #3037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| C2×#951 | 2 |
| C2×C4×Dic6 | 2 |
| #5232 | 2 |
| #5090 | 2 |
| #5075 | 2 |
| #5054 | 2 |
| #4924 | 2 |
| #3037 | 3 |