Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D47 | C2 | semidirect |
| 3. #13094056 | C2 | direct (N × H) |
| 4. C2×#10625337 | C2 | semidirect |
| 5. C2×#10625325 | C2 | semidirect |
| 6. C2×#10625336 | C2 | semidirect |
| 7. C2×#10625324 | C2 | semidirect |
| 8. C2×Q16×C47 | C2 | semidirect |
| 14. Q8×D47 | C22 | semidirect |
| 22. Q16×C47 | C22 | semidirect |
| 24. #10625337 | C22 | semidirect |
| 25. #10625336 | C22 | semidirect |
| 27. #10625325 | C22 | semidirect |
| 28. #10625324 | C22 | semidirect |
| 63. C2×C47 | #137 | semidirect |
| 68. C47 | C2×#137 | semidirect |
| 73. C2×Q16 | D47 | semidirect |
| 91. Q16 | C2×D47 | semidirect |
| 133. C2 | #13094056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625354 | 2 |
| C2×Q8×D47 | 2 |
| #13094056 | 2 |
| C2×#10625337 | 2 |
| C2×#10625325 | 2 |
| C2×#10625336 | 2 |
| C2×#10625324 | 2 |
| C2×Q16×C47 | 2 |
| C2×#137 | 47 |