Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 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×#22627654 | C2 | semidirect |
| 2. C2×#22627649 | C2 | semidirect |
| 3. C2×#22627612 | C2 | semidirect |
| 4. #34036521 | C2 | semidirect |
| 5. #34036516 | C2 | semidirect |
| 6. #34036511 | C2 | semidirect |
| 7. C4×#17989786 | C2 | semidirect |
| 8. #532×C293 | C2 | semidirect |
| 13. C2×#17989792 | C22 | semidirect |
| 14. C2×#17989790 | C22 | semidirect |
| 22. #22627535 | C22 | semidirect |
| 23. C4×#14556873 | C22 | semidirect |
| 25. C4⋊Q8×C293 | C22 | semidirect |
| 26. #127×C293 | C22 | semidirect |
| 27. #124×C293 | C22 | semidirect |
| 43. #17989786 | D4 | semidirect |
| 106. C293 | #3153 | semidirect |
| 110. #532 | D293 | semidirect |
| 126. C4⋊Q8 | C2×D293 | semidirect |
| 127. #127 | C2×D293 | semidirect |
| 131. #124 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627654 | 2 |
| C2×#22627649 | 2 |
| C2×#22627612 | 2 |
| #34036521 | 2 |
| #34036516 | 2 |
| #34036511 | 2 |
| C4×#17989786 | 2 |
| #532×C293 | 2 |
| #3153 | 293 |