Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic6 | C2 | semidirect |
| 5. #4535 | C2 | semidirect |
| 6. #4484 | C2 | semidirect |
| 7. #4481 | C2 | semidirect |
| 77. C3×Q8 | SD16 | semidirect |
| 94. Dic6 | SD16 | semidirect |
| 143. Q8 | #214 | semidirect |
| 178. C3 | #1623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic6 | 2 |
| C3×#460 | 2 |
| #5076 | 2 |
| #5075 | 2 |
| #4535 | 2 |
| #4484 | 2 |
| #4481 | 2 |
| #1623 | 3 |