Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D293 |
| commutator, socle, cosocle | C22×C293 | C25 |
| Fitting | H(3,𝔽4)×C293 | C2 |
| hypercenter | H(3,𝔽4) | D293 |
| hypocenter | C293 | #3529 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #34036879 | C2 | semidirect |
| 2. #34036873 | C2 | semidirect |
| 3. #34036868 | C2 | semidirect |
| 4. #34036678 | C2 | semidirect |
| 5. #34036658 | C2 | semidirect |
| 6. #34036635 | C2 | semidirect |
| 7. H(3,𝔽4)×C293 | C2 | semidirect |
| 8. C2×#17989803 | C22 | semidirect |
| 10. C23×Dic293 | C22 | semidirect |
| 11. #22627622 | C22 | semidirect |
| 13. #22627617 | C22 | semidirect |
| 14. #22627616 | C22 | semidirect |
| 15. #22627612 | C22 | semidirect |
| 16. #22627608 | C22 | semidirect |
| 17. #22627606 | C22 | semidirect |
| 19. #22627601 | C22 | semidirect |
| 20. #22627600 | C22 | semidirect |
| 21. #22627597 | C22 | semidirect |
| 24. #22627593 | C22 | semidirect |
| 25. Q8×Dic293 | C22 | semidirect |
| 27. #22627584 | C22 | semidirect |
| 28. #22627580 | C22 | semidirect |
| 29. C42×D293 | C22 | semidirect |
| 97. C293 | #3529 | semidirect |
| 101. H(3,𝔽4) | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036879 | 2 |
| #34036873 | 2 |
| #34036868 | 2 |
| #34036678 | 2 |
| #34036658 | 2 |
| #34036635 | 2 |
| H(3,𝔽4)×C293 | 2 |
| #3529 | 293 |