Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
616 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 253 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. C22×C8×D37 | C2 | semidirect |
| 3. #14557598 | C2 | direct (N × H) |
| 4. C2×#11924448 | C2 | semidirect |
| 5. C2×C4×#64436 | C2 | semidirect |
| 6. C2×C4⋊C8×C37 | C2 | semidirect |
| 12. C2×C8×D37 | C22 | semidirect |
| 17. #11924448 | C22 | semidirect |
| 18. C4×#64436 | C22 | semidirect |
| 21. C4⋊C8×C37 | C22 | semidirect |
| 27. C2×D148 | C8 | semidirect |
| 40. C2×#64436 | D4 | semidirect |
| 47. C22×D37 | C2×C8 | semidirect |
| 50. C2×C4×C37 | C2×C8 | semidirect |
| 59. D148 | C2×C8 | semidirect |
| 65. #64436 | C2×D4 | semidirect |
| 73. C2×D37 | C22×C8 | semidirect |
| 76. C4×C37 | C22×C8 | semidirect |
| 81. C2×C37 | C8×D4 | semidirect |
| 89. C2×C4⋊C8 | D37 | semidirect |
| 92. C37 | C2×C8×D4 | semidirect |
| 105. C4⋊C8 | C2×D37 | semidirect |
| 142. C2×C4 | C8×D37 | semidirect |
| 163. C4 | C2×C8×D37 | semidirect |
| 167. C2 | #14557598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D37 | 2 |
| C2×C4×D148 | 2 |
| #14557598 | 2 |
| C2×#11924448 | 2 |
| C2×C4×#64436 | 2 |
| C2×C4⋊C8×C37 | 2 |
| C2×C8×D4 | 37 |