Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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×#22627711 | C2 | semidirect |
| 2. #34037164 | C2 | semidirect |
| 3. #34037160 | C2 | semidirect |
| 4. D4×#14556880 | C2 | semidirect |
| 5. D293⋊(C4⋊C8) | C2 | semidirect |
| 6. #34037103 | C2 | semidirect |
| 7. C4×#17989812 | C2 | semidirect |
| 32. #17989812 | D4 | semidirect |
| 92. C4×C293 | #131 | semidirect |
| 103. C293 | #2935 | semidirect |
| 201. C4 | #22627711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627711 | 2 |
| #34037164 | 2 |
| #34037160 | 2 |
| D4×#14556880 | 2 |
| D293⋊(C4⋊C8) | 2 |
| #34037103 | 2 |
| C4×#17989812 | 2 |
| #34036677 | 2 |
| #2935 | 293 |