Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
180 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 56 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. #34037164 | C2 | semidirect |
| 2. #34037163 | C2 | semidirect |
| 3. #34036993 | C2 | semidirect |
| 4. #34036977 | C2 | semidirect |
| 5. D4⋊#14556880 | C2 | semidirect |
| 6. C8×#14556880 | C2 | semidirect |
| 46. #14556880 | D8 | semidirect |
| 57. #14556873 | M16 | semidirect |
| 83. C293 | #1589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037164 | 2 |
| #34037163 | 2 |
| #34036993 | 2 |
| #34036977 | 2 |
| D4⋊#14556880 | 2 |
| C8×#14556880 | 2 |
| #34036209 | 2 |
| #1589 | 293 |