Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic74 | C2 | semidirect |
| 5. #14557281 | C2 | semidirect |
| 6. #14557265 | C2 | semidirect |
| 7. C37×Q8⋊C8 | C2 | semidirect |
| 52. Q8×C37 | SD16 | semidirect |
| 69. Dic74 | SD16 | semidirect |
| 98. Q8⋊C8 | D37 | semidirect |
| 99. C37 | #1623 | semidirect |
| 148. Q8 | #10596930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic74 | 2 |
| #14557906 | 2 |
| #14557734 | 2 |
| #14557733 | 2 |
| #14557281 | 2 |
| #14557265 | 2 |
| C37×Q8⋊C8 | 2 |
| #1623 | 37 |