Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22627655 | C2 | semidirect |
| 3. #34036521 | C2 | semidirect |
| 4. #34036508 | C2 | semidirect |
| 5. #34036503 | C2 | semidirect |
| 6. C4×#17989786 | C2 | semidirect |
| 7. C2×C4⋊Q8×C293 | C2 | semidirect |
| 34. #17989786 | D4 | semidirect |
| 76. C4×C293 | #137 | semidirect |
| 83. C293 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D293 | semidirect |
| 161. C4 | #22627655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627655 | 2 |
| #34036679 | 2 |
| #34036521 | 2 |
| #34036508 | 2 |
| #34036503 | 2 |
| C4×#17989786 | 2 |
| C2×C4⋊Q8×C293 | 2 |
| #3152 | 293 |