Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 316 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 |
| 3. #5131 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. #5101 | C2 | semidirect |
| 15. C2×D24 | C4 | semidirect |
| 22. C2×#108 | D3 | semidirect |
| 157. C3 | #1978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×C3×#108 | 2 |
| #5131 | 2 |
| C2×#823 | 2 |
| #5101 | 2 |
| #1978 | 3 |