Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
256 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 89 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×C3×#108 | C2 | semidirect |
| 4. #5106 | C2 | semidirect |
| 5. #4556 | C2 | semidirect |
| 14. #901 | C4 | semidirect |
| 15. #901 | C4 | semidirect |
| 24. C2×#108 | D3 | semidirect |
| 177. C3 | #1814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| C2×C3×#108 | 2 |
| #5139 | 2 |
| #5106 | 2 |
| #4556 | 2 |
| #1814 | 3 |