Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22627646 | C2 | semidirect |
| 2. #34036679 | C2 | semidirect |
| 3. #34036513 | C2 | semidirect |
| 4. #34036509 | C2 | semidirect |
| 5. #34036506 | C2 | semidirect |
| 6. #34036502 | C2 | semidirect |
| 7. C2×C4×C8×C293 | C2 | semidirect |
| 36. C2×C8×C293 | D4 | semidirect |
| 65. C4×C293 | #135 | semidirect |
| 72. C293 | #3147 | semidirect |
| 80. C2×C4×C8 | D293 | semidirect |
| 107. C2×C8 | D1172 | semidirect |
| 139. C4 | #22627646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627646 | 2 |
| #34036679 | 2 |
| #34036513 | 2 |
| #34036509 | 2 |
| #34036506 | 2 |
| #34036502 | 2 |
| C2×C4×C8×C293 | 2 |
| #3147 | 293 |