Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10596940 | C2 | semidirect |
| 2. C22×#10596939 | C2 | semidirect |
| 3. C2×#11924524 | C2 | semidirect |
| 4. #14557920 | C2 | direct (N × H) |
| 5. C2×#11924447 | C2 | semidirect |
| 6. C2×#127×C37 | C2 | semidirect |
| 10. C2×#10596940 | C22 | semidirect |
| 12. C2×#10596939 | C22 | semidirect |
| 15. #11924524 | C22 | semidirect |
| 17. #11924447 | C22 | semidirect |
| 21. #127×C37 | C22 | semidirect |
| 45. C2×#64436 | D4 | semidirect |
| 69. #64436 | C2×D4 | semidirect |
| 85. C2×C37 | #496 | semidirect |
| 91. C2×#127 | D37 | semidirect |
| 95. C37 | C2×#496 | semidirect |
| 106. #127 | C2×D37 | semidirect |
| 174. C2 | #14557920 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596940 | 2 |
| C22×#10596939 | 2 |
| C2×#11924524 | 2 |
| #14557920 | 2 |
| C2×#11924447 | 2 |
| C2×#127×C37 | 2 |
| C2×#496 | 37 |