Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. #14557905 | C2 | semidirect |
| 2. #14557828 | C2 | semidirect |
| 3. #14557823 | C2 | semidirect |
| 4. #14557277 | C2 | semidirect |
| 5. Q8⋊#64436 | C2 | semidirect |
| 6. D4⋊#64436 | C2 | semidirect |
| 53. Q8×C37 | SD16 | semidirect |
| 106. C37 | #1631 | semidirect |
| 153. Q8 | #10596940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557905 | 2 |
| #14557828 | 2 |
| #14557823 | 2 |
| #14557277 | 2 |
| Q8⋊#64436 | 2 |
| D4⋊#64436 | 2 |
| C37×#550 | 2 |
| #1631 | 37 |