Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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. #5517 | C2 | semidirect |
| 5. #4533 | C2 | semidirect |
| 6. #4532 | C2 | semidirect |
| 7. #4531 | C2 | semidirect |
| 35. C2×C3×Q8 | Q8 | semidirect |
| 37. C2×C3×D4 | Q8 | semidirect |
| 109. C2×Q8 | Dic6 | semidirect |
| 111. C2×D4 | Dic6 | semidirect |
| 199. C3 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5517 | 2 |
| C3×#410 | 2 |
| #5236 | 2 |
| C2×#837 | 2 |
| #4533 | 2 |
| #4532 | 2 |
| #4531 | 2 |
| #2031 | 3 |