Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11924533 | C2 | semidirect |
| 3. #14557733 | C2 | semidirect |
| 4. #14557728 | C2 | semidirect |
| 5. #14557557 | C2 | semidirect |
| 6. #14557537 | C2 | semidirect |
| 7. C4×#41×C37 | C2 | semidirect |
| 11. C2×#10596941 | C22 | semidirect |
| 12. C2×#10596939 | C22 | semidirect |
| 17. C4⋊#64436 | C22 | semidirect |
| 18. #11924456 | C22 | semidirect |
| 20. C4×Q8×C37 | C22 | semidirect |
| 22. C4×D4×C37 | C22 | semidirect |
| 29. #41×C37 | D4 | semidirect |
| 63. Q8×C37 | C2×D4 | semidirect |
| 66. D4×C37 | C2×D4 | semidirect |
| 96. C4×C37 | AGL(1,ℤ/8) | semidirect |
| 107. C4×#41 | D37 | semidirect |
| 112. C37 | #3038 | semidirect |
| 123. C4×Q8 | C2×D37 | semidirect |
| 125. C4×D4 | C2×D37 | semidirect |
| 134. #41 | D148 | semidirect |
| 168. Q8 | C2×D148 | semidirect |
| 176. D4 | C2×D148 | semidirect |
| 201. 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×#11924533 | 2 |
| #14557733 | 2 |
| #14557728 | 2 |
| #14557557 | 2 |
| #14557537 | 2 |
| C4×#41×C37 | 2 |
| #3038 | 37 |