Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
688 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 152 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. #34037081 | C2 | semidirect |
| 2. #34037079 | C2 | semidirect |
| 3. #34037077 | C2 | semidirect |
| 4. #34037070 | C2 | semidirect |
| 6. C23×#11924078 | C22 | semidirect |
| 7. C2×C4⋊#11924078 | C22 | semidirect |
| 10. C2×C22⋊#11924078 | C22 | semidirect |
| 11. C2×C4×#11924078 | C22 | semidirect |
| 12. (C2×#11924078)⋊C4 | C22 | semidirect |
| 15. #22627594 | C4 | semidirect |
| 16. #22627593 | C4 | semidirect |
| 17. #22627592 | C4 | semidirect |
| 19. #120×C293 | C4 | semidirect |
| 30. C23×D293 | C2×C4 | semidirect |
| 39. C22⋊Dic293 | C2×C4 | semidirect |
| 40. #17989779 | C2×C4 | semidirect |
| 41. C24×C293 | C2×C4 | semidirect |
| 43. C22⋊C4×C293 | C2×C4 | semidirect |
| 100. C293 | #2375 | semidirect |
| 113. #120 | #11924078 | semidirect |
| 126. C24 | C2×#11924078 | semidirect |
| 143. C22⋊C4 | C2×#11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037081 | 2 |
| #34037079 | 2 |
| #34037077 | 2 |
| #34037070 | 2 |
| #120×D293 | 2 |
| #2375 | 293 |