Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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. #14558089 | C2 | direct (N × H) |
| 2. C2×#11924535 | C2 | semidirect |
| 3. C2×#11924528 | C2 | semidirect |
| 5. C2×#11924501 | C2 | semidirect |
| 8. C2×#125×C37 | C2 | semidirect |
| 12. #11924535 | C22 | semidirect |
| 13. #11924528 | C22 | semidirect |
| 15. #11924501 | C22 | semidirect |
| 25. #125×C37 | C22 | semidirect |
| 37. C2×C4×D37 | Q8 | semidirect |
| 69. C4×D37 | C2×Q8 | semidirect |
| 84. C2×C37 | #533 | semidirect |
| 91. C2×#125 | D37 | semidirect |
| 96. C37 | C2×#533 | semidirect |
| 102. #125 | C2×D37 | semidirect |
| 172. C2 | #14558089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558089 | 2 |
| C2×#11924535 | 2 |
| C2×#11924528 | 2 |
| C2×#11924514 | 2 |
| C2×#11924501 | 2 |
| C2×#11924494 | 2 |
| C2×C42×D37 | 2 |
| C2×#125×C37 | 2 |
| C2×#533 | 37 |