Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#17989790 | C2 | semidirect |
| 3. C2×#22627612 | C2 | semidirect |
| 4. #34036344 | C2 | direct (N × H) |
| 5. C2×C4⋊#14556873 | C2 | semidirect |
| 6. C2×#22627547 | C2 | semidirect |
| 7. C2×#22627544 | C2 | semidirect |
| 8. C2×C4×D4×C293 | C2 | semidirect |
| 12. C2×#17989790 | C22 | semidirect |
| 18. #22627612 | C22 | semidirect |
| 21. C4⋊#14556873 | C22 | semidirect |
| 22. #22627547 | C22 | semidirect |
| 23. #22627544 | C22 | semidirect |
| 27. C4×D4×C293 | C22 | semidirect |
| 118. C2×C293 | #463 | semidirect |
| 123. C293 | C2×#463 | semidirect |
| 128. C2×C4×D4 | D293 | semidirect |
| 146. C4×D4 | C2×D293 | semidirect |
| 243. C2 | #34036344 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17989790 | 2 |
| C22×#17989787 | 2 |
| C2×#22627612 | 2 |
| #34036344 | 2 |
| C2×C4⋊#14556873 | 2 |
| C2×#22627547 | 2 |
| C2×#22627544 | 2 |
| C2×C4×D4×C293 | 2 |
| C2×#463 | 293 |