Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22627644 | C2 | semidirect |
| 3. #34036675 | C2 | semidirect |
| 4. #34036522 | C2 | semidirect |
| 5. #34036520 | C2 | semidirect |
| 6. #34036517 | C2 | semidirect |
| 7. #34036515 | C2 | semidirect |
| 8. C2×#22627534 | C2 | semidirect |
| 9. C2×#135×C293 | C2 | semidirect |
| 51. C2×#14556873 | D4 | semidirect |
| 68. C2×C8×C293 | D4 | semidirect |
| 116. C293 | #3150 | semidirect |
| 120. C2×#135 | D293 | semidirect |
| 180. C2×C8 | C22⋊D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627646 | 2 |
| C2×#22627644 | 2 |
| #34036675 | 2 |
| #34036522 | 2 |
| #34036520 | 2 |
| #34036517 | 2 |
| #34036515 | 2 |
| C2×#22627534 | 2 |
| C2×#135×C293 | 2 |
| #3150 | 293 |