Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #34036682 | C2 | semidirect |
| 3. #34036492 | C2 | semidirect |
| 4. #34036474 | C2 | semidirect |
| 5. #34036135 | C2 | semidirect |
| 6. #34036134 | C2 | semidirect |
| 7. #34036133 | C2 | semidirect |
| 8. M16×Dic293 | C2 | semidirect |
| 9. #418×C293 | C2 | semidirect |
| 13. #22627623 | C22 | semidirect |
| 17. #22627615 | C22 | semidirect |
| 22. #22627546 | C22 | semidirect |
| 23. #22627545 | C22 | semidirect |
| 24. #22627544 | C22 | semidirect |
| 25. #22627534 | C22 | semidirect |
| 26. C8×Dic293 | C22 | semidirect |
| 30. #102×C293 | C22 | semidirect |
| 111. C293 | #3138 | semidirect |
| 120. #418 | D293 | semidirect |
| 140. #102 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036682 | 2 |
| C2×#22627620 | 2 |
| #34036492 | 2 |
| #34036474 | 2 |
| #34036135 | 2 |
| #34036134 | 2 |
| #34036133 | 2 |
| M16×Dic293 | 2 |
| #418×C293 | 2 |
| #3138 | 293 |