Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #34036684 | C2 | semidirect |
| 3. #34036463 | C2 | semidirect |
| 4. #34036410 | C2 | semidirect |
| 5. #34036409 | C2 | semidirect |
| 6. #34036331 | C2 | semidirect |
| 8. #34036232 | C2 | semidirect |
| 9. #34036230 | C2 | semidirect |
| 10. #34036185 | C2 | semidirect |
| 11. #461×C293 | C2 | semidirect |
| 15. #22627624 | C22 | semidirect |
| 19. Q8×Dic293 | C22 | semidirect |
| 30. #22627558 | C22 | semidirect |
| 31. #22627557 | C22 | semidirect |
| 32. C4⋊#14556873 | C22 | semidirect |
| 33. #22627548 | C22 | semidirect |
| 37. #22627534 | C22 | semidirect |
| 39. C4⋊Q8×C293 | C22 | semidirect |
| 41. C4⋊C8×C293 | C22 | semidirect |
| 42. #103×C293 | C22 | semidirect |
| 146. C293 | #3110 | semidirect |
| 154. #461 | D293 | semidirect |
| 164. C4⋊Q8 | C2×D293 | semidirect |
| 183. C4⋊C8 | C2×D293 | semidirect |
| 185. #103 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036684 | 2 |
| C4×D4×D293 | 2 |
| #34036463 | 2 |
| #34036410 | 2 |
| #34036409 | 2 |
| #34036331 | 2 |
| #34036278 | 2 |
| #34036232 | 2 |
| #34036230 | 2 |
| #34036185 | 2 |
| #461×C293 | 2 |
| #3110 | 293 |