Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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. C3×C8×Q8 | C2 | semidirect |
| 4. #4535 | C2 | semidirect |
| 6. #4480 | C2 | semidirect |
| 7. #4455 | C2 | semidirect |
| 24. C8×Q8 | D3 | semidirect |
| 66. C3×Q8 | M16 | semidirect |
| 79. C3×C8 | SD16 | semidirect |
| 116. Q8 | ΓL(1,𝔽25) | semidirect |
| 133. C8 | #215 | semidirect |
| 150. C3 | #1583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Q8 | 2 |
| C4×#215 | 2 |
| #4688 | 2 |
| #4535 | 2 |
| #4483 | 2 |
| #4480 | 2 |
| #4455 | 2 |
| #1583 | 3 |