Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#427 | C2 | semidirect |
| 3. #5106 | C2 | semidirect |
| 5. #4531 | C2 | semidirect |
| 16. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 17. C2×D3×C8 | C4 | semidirect |
| 25. #427 | D3 | semidirect |
| 179. C3 | #1812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| C3×#427 | 2 |
| #5106 | 2 |
| #5006 | 2 |
| #4531 | 2 |
| #1812 | 3 |