Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #34036686 | C2 | semidirect |
| 3. #34036494 | C2 | semidirect |
| 4. #34036476 | C2 | semidirect |
| 5. #34036135 | C2 | semidirect |
| 6. C4×M16×C293 | C2 | semidirect |
| 9. #22627624 | C22 | semidirect |
| 13. #22627616 | C22 | semidirect |
| 17. #22627546 | C22 | semidirect |
| 20. #97×C293 | C22 | semidirect |
| 21. C4×C8×C293 | C22 | semidirect |
| 74. C293 | #3138 | semidirect |
| 81. C4×M16 | D293 | semidirect |
| 95. #97 | C2×D293 | semidirect |
| 96. C4×C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036686 | 2 |
| C2×#22627621 | 2 |
| #34036494 | 2 |
| #34036476 | 2 |
| #34036135 | 2 |
| C4×M16×C293 | 2 |
| #3138 | 293 |