Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
708 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 708 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. C2×#11924566 | C2 | semidirect |
| 2. C2×#11924534 | C2 | semidirect |
| 3. #14557716 | C2 | direct (N × H) |
| 4. C2×#11924463 | C2 | semidirect |
| 5. C2×#11924455 | C2 | semidirect |
| 9. #11924566 | C22 | semidirect |
| 14. #11924534 | C22 | semidirect |
| 17. #11924463 | C22 | semidirect |
| 18. #11924455 | C22 | semidirect |
| 111. C2×C37 | #456 | semidirect |
| 119. C37 | C2×#456 | semidirect |
| 223. C2 | #14557716 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924566 | 2 |
| C2×#11924534 | 2 |
| #14557716 | 2 |
| C2×#11924463 | 2 |
| C2×#11924455 | 2 |
| C2×2−1+4×C37 | 2 |
| C2×#456 | 37 |