Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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. #41×#11924078 | C2 | semidirect |
| 2. #34037126 | C2 | semidirect |
| 3. C2×#22627689 | C2 | semidirect |
| 4. #34037110 | C2 | semidirect |
| 5. #34037012 | C2 | semidirect |
| 6. #34037001 | C2 | semidirect |
| 25. #22627655 | C4 | semidirect |
| 26. #22627652 | C4 | semidirect |
| 28. #22627649 | C4 | semidirect |
| 32. #137×C293 | C4 | semidirect |
| 61. C2×D1172 | C2×C4 | semidirect |
| 73. #17989786 | C2×C4 | semidirect |
| 77. C2×Q8×C293 | C2×C4 | semidirect |
| 80. M16×C293 | C2×C4 | semidirect |
| 150. C293 | #1906 | semidirect |
| 163. #137 | #11924078 | semidirect |
| 195. C2×Q8 | C2×#11924078 | semidirect |
| 217. M16 | C2×#11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#11924078 | 2 |
| #34037126 | 2 |
| C2×#22627689 | 2 |
| #34037110 | 2 |
| #34037012 | 2 |
| #34037001 | 2 |
| #34036928 | 2 |
| #1906 | 293 |