Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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×#11924624 | C2 | semidirect |
| 2. #14558567 | C2 | semidirect |
| 3. #14558563 | C2 | semidirect |
| 4. #14558561 | C2 | semidirect |
| 5. D37⋊(C4⋊C8) | C2 | semidirect |
| 6. #14558508 | C2 | semidirect |
| 7. C4×#10596953 | C2 | semidirect |
| 48. #10596953 | D4 | semidirect |
| 93. C4×C37 | #131 | semidirect |
| 112. C37 | #2935 | semidirect |
| 201. C4 | #11924624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924624 | 2 |
| #14558567 | 2 |
| #14558563 | 2 |
| #14558561 | 2 |
| D37⋊(C4⋊C8) | 2 |
| #14558508 | 2 |
| C4×#10596953 | 2 |
| #14558084 | 2 |
| #2935 | 37 |