Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #34037175 | C2 | semidirect |
| 2. #34037170 | C2 | semidirect |
| 3. #34037054 | C2 | semidirect |
| 4. #34037047 | C2 | semidirect |
| 5. #34037046 | C2 | semidirect |
| 6. #34037019 | C2 | semidirect |
| 18. #22627567 | C4 | semidirect |
| 19. D4688 | C4 | semidirect |
| 20. #22627565 | C4 | semidirect |
| 22. SD32×C293 | C4 | semidirect |
| 36. D2344 | C2×C4 | semidirect |
| 39. #17989777 | C2×C4 | semidirect |
| 40. Q16×C293 | C2×C4 | semidirect |
| 42. C16×C293 | C2×C4 | semidirect |
| 75. C293 | AGL(1,ℤ/16) | semidirect |
| 89. SD32 | #11924078 | semidirect |
| 102. Q16 | C2×#11924078 | semidirect |
| 118. C16 | C2×#11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037175 | 2 |
| #34037170 | 2 |
| #34037054 | 2 |
| #34037047 | 2 |
| #34037046 | 2 |
| #34037019 | 2 |
| #34036566 | 2 |
| AGL(1,ℤ/16) | 293 |