Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D293 | C2 | semidirect |
| 3. #34036423 | C2 | semidirect |
| 4. #34036417 | C2 | semidirect |
| 5. #34036415 | C2 | semidirect |
| 6. #34036411 | C2 | semidirect |
| 7. #34036409 | C2 | semidirect |
| 8. #34036170 | C2 | semidirect |
| 9. #34036151 | C2 | semidirect |
| 11. #474×C293 | C2 | semidirect |
| 44. #17989801 | Q8 | semidirect |
| 86. Dic586 | C2×Q8 | semidirect |
| 105. D4×C293 | C2×Q8 | semidirect |
| 137. C293 | #3079 | semidirect |
| 146. #474 | D293 | semidirect |
| 229. D4 | Q8×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D293 | 2 |
| C4×#17989801 | 2 |
| #34036423 | 2 |
| #34036417 | 2 |
| #34036415 | 2 |
| #34036411 | 2 |
| #34036409 | 2 |
| #34036170 | 2 |
| #34036151 | 2 |
| #34036127 | 2 |
| #474×C293 | 2 |
| #3079 | 293 |