Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
528 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 234 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. #34037147 | C2 | direct (N × H) |
| 2. C2×#22627691 | C2 | semidirect |
| 4. C2×C4×#14556880 | C2 | semidirect |
| 7. #22627691 | C22 | semidirect |
| 9. C4×#14556880 | C22 | semidirect |
| 27. C2×C4×D293 | C8 | semidirect |
| 56. C4×D293 | C2×C8 | semidirect |
| 79. C2×C293 | #431 | semidirect |
| 84. C293 | C2×#431 | semidirect |
| 165. C2 | #34037147 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037147 | 2 |
| C2×#22627691 | 2 |
| C2×#22627681 | 2 |
| C2×C4×#14556880 | 2 |
| C2×C42×D293 | 2 |
| C2×#431 | 293 |