Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. #13094023 | C2 | semidirect |
| 2. #13094014 | C2 | semidirect |
| 3. #13094004 | C2 | semidirect |
| 4. #13094003 | C2 | semidirect |
| 5. #13094003 | C2 | semidirect |
| 6. #13094002 | C2 | semidirect |
| 7. #13093989 | C2 | semidirect |
| 10. C4⋊C4×D47 | C2 | semidirect |
| 11. C2×C4⋊C4×C47 | C2 | semidirect |
| 43. C22⋊D47 | Q8 | semidirect |
| 75. C47 | #554 | semidirect |
| 86. C2×C4⋊C4 | D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13094023 | 2 |
| #13094014 | 2 |
| #13094004 | 2 |
| #13094003 | 2 |
| #13094002 | 2 |
| #13093989 | 2 |
| C4×C22⋊D47 | 2 |
| C4⋊C4×D47 | 2 |
| C2×C4⋊C4×C47 | 2 |
| #554 | 47 |