Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #5122 | C2 | semidirect |
| 5. #4997 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. #4556 | C2 | semidirect |
| 20. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 21. C2×D3×C8 | C4 | semidirect |
| 22. #824 | C4 | semidirect |
| 23. #823 | C4 | semidirect |
| 35. #344 | D3 | semidirect |
| 207. C3 | #1757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#907 | 2 |
| #5132 | 2 |
| #5122 | 2 |
| #5006 | 2 |
| #4997 | 2 |
| C3×#344 | 2 |
| #4556 | 2 |
| #1757 | 3 |