Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
166 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 58 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. Q8×#14556880 | C2 | semidirect |
| 3. #34036991 | C2 | semidirect |
| 4. Q8⋊#14556880 | C2 | semidirect |
| 6. #14556880⋊C8 | C2 | semidirect |
| 45. #14556880 | SD16 | semidirect |
| 55. Q8×C293 | M16 | semidirect |
| 77. C293 | #1583 | semidirect |
| 121. Q8 | #17989811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#14556880 | 2 |
| #34037164 | 2 |
| #34036991 | 2 |
| Q8⋊#14556880 | 2 |
| D4⋊#14556880 | 2 |
| #14556880⋊C8 | 2 |
| SD16×Dic293 | 2 |
| #1583 | 293 |