Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C2×Q8×Dic3 | C2 | semidirect |
| 3. C2×C3×#103 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 17. C2×#215 | C4 | semidirect |
| 29. C2×#103 | D3 | semidirect |
| 99. C3×Q8 | C22⋊C4 | semidirect |
| 120. C2×Dic3 | SD16 | semidirect |
| 197. Q8 | (C2×D3)⋊C4 | semidirect |
| 256. C3 | #1880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic3 | 2 |
| C22×#215 | 2 |
| C2×C3×#103 | 2 |
| C2×#821 | 2 |
| #4988 | 2 |
| #4550 | 2 |
| #4529 | 2 |
| #1880 | 3 |