Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 2. #4688 | C2 | semidirect |
| 3. C3×C82 | C2 | semidirect |
| 4. #4459 | C2 | semidirect |
| 5. #4458 | C2 | semidirect |
| 21. C82 | D3 | semidirect |
| 57. C3×C8 | M16 | semidirect |
| 58. C3×C8 | D8 | semidirect |
| 96. C8 | ΓL(1,𝔽25) | semidirect |
| 97. C8 | D24 | semidirect |
| 112. C3 | #1589 | 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×C82 | 2 |
| #4459 | 2 |
| #4458 | 2 |
| #1589 | 3 |