Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
500 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 189 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×#11924544 | C2 | semidirect |
| 3. #14557610 | C2 | semidirect |
| 4. #14557598 | C2 | semidirect |
| 5. #14557501 | C2 | semidirect |
| 6. C2×C4×#64436 | C2 | semidirect |
| 7. C37×#423 | C2 | semidirect |
| 42. C2×#64436 | D4 | semidirect |
| 75. C4×C37 | #131 | semidirect |
| 88. #423 | D37 | semidirect |
| 91. C37 | #2931 | semidirect |
| 160. C4 | #11924544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924544 | 2 |
| #14558083 | 2 |
| #14557610 | 2 |
| #14557598 | 2 |
| #14557501 | 2 |
| C2×C4×#64436 | 2 |
| C37×#423 | 2 |
| #2931 | 37 |