Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 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. #34036679 | C2 | semidirect |
| 2. #34036532 | C2 | semidirect |
| 3. #34036505 | C2 | semidirect |
| 4. #34036477 | C2 | semidirect |
| 5. #34036475 | C2 | semidirect |
| 6. #34036363 | C2 | semidirect |
| 7. C4×#17989787 | C2 | semidirect |
| 8. C2×C4×#14556873 | C2 | semidirect |
| 9. #532×C293 | C2 | semidirect |
| 77. #14556873 | #41 | semidirect |
| 89. C2×C4×C293 | D8 | semidirect |
| 120. C293 | #3169 | semidirect |
| 123. #532 | D293 | semidirect |
| 208. C2×C4 | #17989787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036679 | 2 |
| #34036532 | 2 |
| #34036505 | 2 |
| #34036477 | 2 |
| #34036475 | 2 |
| #34036363 | 2 |
| C4×#17989787 | 2 |
| C2×C4×#14556873 | 2 |
| #532×C293 | 2 |
| #3169 | 293 |