Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 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. #14558585 | C2 | semidirect |
| 2. #14558584 | C2 | semidirect |
| 3. Q8×#64438 | C2 | semidirect |
| 40. #10596953 | Q8 | semidirect |
| 99. C37 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558585 | 2 |
| #14558584 | 2 |
| Q8×#64438 | 2 |
| #14558540 | 2 |
| D37⋊(C4⋊C8) | 2 |
| #14558498 | 2 |
| C4×#10596953 | 2 |
| #14558088 | 2 |
| #2962 | 37 |