Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
336 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#22627678 | C2 | semidirect |
| 4. C2×C8×#11924078 | C2 | semidirect |
| 5. (C2×#11924078)⋊C8 | C2 | semidirect |
| 6. (C2×#11924078)⋊C8 | C2 | semidirect |
| 16. #22627681 | C4 | semidirect |
| 17. C22⋊#14556880 | C4 | semidirect |
| 23. C22⋊#14556873 | C4 | semidirect |
| 24. #22627536 | C4 | semidirect |
| 25. #22627536 | C4 | semidirect |
| 26. C22⋊C8×C293 | C4 | semidirect |
| 125. C293 | #1750 | semidirect |
| 150. C22⋊C8 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627703 | 2 |
| D293⋊(C22⋊C8) | 2 |
| C2×#22627678 | 2 |
| C2×C8×#11924078 | 2 |
| (C2×#11924078)⋊C8 | 2 |
| C22⋊C8×D293 | 2 |
| #1750 | 293 |