Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #5522 | C2 | semidirect |
| 3. C3×#410 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5005 | C2 | semidirect |
| 6. #4533 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 16. #942 | C4 | semidirect |
| 17. #932 | C4 | semidirect |
| 34. #410 | D3 | semidirect |
| 41. C2×C3×Q8 | C2×C4 | semidirect |
| 43. C2×C3×D4 | C2×C4 | semidirect |
| 75. #208 | C2×C4 | semidirect |
| 143. C2×Q8 | C4×D3 | semidirect |
| 147. C2×D4 | C4×D3 | semidirect |
| 252. C3 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5822 | 2 |
| #5522 | 2 |
| C3×#410 | 2 |
| C2×#837 | 2 |
| #5005 | 2 |
| #4533 | 2 |
| #4532 | 2 |
| #1906 | 3 |