Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#11924561 | C2 | semidirect |
| 2. C2×C4×D148 | C2 | semidirect |
| 3. #14557745 | C2 | semidirect |
| 4. #14557735 | C2 | semidirect |
| 5. #14557725 | C2 | semidirect |
| 6. #14557557 | C2 | semidirect |
| 7. #14557534 | C2 | semidirect |
| 8. C37×#532 | C2 | semidirect |
| 21. C4⋊#64436 | C22 | semidirect |
| 22. C4⋊#64436 | C22 | semidirect |
| 23. #11924460 | C22 | semidirect |
| 24. #11924457 | C22 | semidirect |
| 26. C4⋊Q8×C37 | C22 | semidirect |
| 27. #127×C37 | C22 | semidirect |
| 28. #124×C37 | C22 | semidirect |
| 49. C2×D148 | D4 | semidirect |
| 119. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 131. #532 | D37 | semidirect |
| 138. C37 | #3036 | semidirect |
| 146. C4⋊Q8 | C2×D37 | semidirect |
| 147. #127 | C2×D37 | semidirect |
| 148. #124 | C2×D37 | semidirect |
| 250. C4 | #11924561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924561 | 2 |
| C2×C4×D148 | 2 |
| #14557745 | 2 |
| #14557735 | 2 |
| #14557725 | 2 |
| #14557557 | 2 |
| #14557534 | 2 |
| C37×#532 | 2 |
| #3036 | 37 |