Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22627649 | C2 | semidirect |
| 2. C22×D2344 | C2 | semidirect |
| 3. #34036693 | C2 | semidirect |
| 4. #34036515 | C2 | semidirect |
| 5. #34036514 | C2 | semidirect |
| 6. #34036504 | C2 | semidirect |
| 7. #34036084 | C2 | semidirect |
| 8. C2×#135×C293 | C2 | semidirect |
| 11. C2×#17989789 | C22 | semidirect |
| 15. C2×#17989787 | C22 | semidirect |
| 17. #22627620 | C22 | semidirect |
| 18. #22627613 | C22 | semidirect |
| 22. #22627534 | C22 | semidirect |
| 23. C8×Dic293 | C22 | semidirect |
| 26. C2×Q16×C293 | C22 | semidirect |
| 27. C2×SD16×C293 | C22 | semidirect |
| 28. C2×D8×C293 | C22 | semidirect |
| 40. #17989786 | D4 | semidirect |
| 56. C2×C8×C293 | D4 | semidirect |
| 101. C293 | #3155 | semidirect |
| 104. C2×#135 | D293 | semidirect |
| 115. C2×Q16 | C2×D293 | semidirect |
| 117. C2×SD16 | C2×D293 | semidirect |
| 122. C2×D8 | C2×D293 | semidirect |
| 154. C2×C8 | C22⋊D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627649 | 2 |
| C22×D2344 | 2 |
| #34036693 | 2 |
| #34036515 | 2 |
| #34036514 | 2 |
| #34036504 | 2 |
| #34036084 | 2 |
| C2×#135×C293 | 2 |
| #3155 | 293 |