Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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. Q8×C3⋊C8 | C2 | semidirect |
| 3. #5012 | C2 | semidirect |
| 4. #4926 | C2 | semidirect |
| 5. C4×#208 | C2 | semidirect |
| 55. C3×Q8 | M16 | semidirect |
| 67. C3⋊C8 | #41 | semidirect |
| 95. Q8 | #208 | semidirect |
| 122. C3 | #2971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41 | 2 |
| Q8×C3⋊C8 | 2 |
| #5012 | 2 |
| #4926 | 2 |
| C4×#208 | 2 |
| #2971 | 3 |