Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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×#405 | C2 | semidirect |
| 4. #5101 | C2 | semidirect |
| 6. #4559 | C2 | semidirect |
| 7. #4533 | C2 | semidirect |
| 20. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 21. C2×D3×C8 | C4 | semidirect |
| 24. #824 | C4 | semidirect |
| 25. #823 | C4 | semidirect |
| 33. #405 | 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×#901 | 2 |
| C3×#405 | 2 |
| #5132 | 2 |
| #5101 | 2 |
| #5006 | 2 |
| #4559 | 2 |
| #4533 | 2 |
| #1757 | 3 |