Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 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 |
|---|---|---|
| 2. #4688 | C2 | semidirect |
| 3. C3×#322 | C2 | semidirect |
| 4. #4459 | C2 | semidirect |
| 5. #4457 | C2 | semidirect |
| 21. #322 | D3 | semidirect |
| 56. C3×C8 | M16 | semidirect |
| 92. C8 | ΓL(1,𝔽25) | semidirect |
| 106. C3 | #1594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D24 | 2 |
| #4688 | 2 |
| C3×#322 | 2 |
| #4459 | 2 |
| #4457 | 2 |
| #1594 | 3 |