Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
1072 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 306 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. C22×D293⋊C8 | C2 | semidirect |
| 2. C2×#22627681 | C2 | semidirect |
| 3. D293⋊(C22⋊C8) | C2 | direct (N × H) |
| 4. C2×C22⋊#14556880 | C2 | semidirect |
| 7. C2×D293⋊C8 | C22 | semidirect |
| 8. C22×#14556880 | C22 | semidirect |
| 9. #22627681 | C22 | semidirect |
| 10. C22⋊#14556880 | C22 | semidirect |
| 23. C2×#14556880 | C23 | semidirect |
| 26. C23×D293 | C8 | semidirect |
| 60. C22×D293 | C2×C8 | semidirect |
| 61. C22×D293 | C2×C8 | semidirect |
| 80. C23×C293 | C2×C8 | semidirect |
| 93. C22×C293 | C22×C8 | semidirect |
| 100. C2×D293 | C22⋊C8 | semidirect |
| 103. C2×D293 | C22×C8 | semidirect |
| 111. C2×C293 | C2×C22⋊C8 | semidirect |
| 116. D293 | C2×C22⋊C8 | semidirect |
| 117. C293 | C22×C22⋊C8 | semidirect |
| 184. C23 | D293⋊C8 | semidirect |
| 220. C22 | C2×D293⋊C8 | semidirect |
| 231. C2 | D293⋊(C22⋊C8) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D293⋊C8 | 2 |
| C2×#22627681 | 2 |
| D293⋊(C22⋊C8) | 2 |
| C2×C22⋊#14556880 | 2 |
| C23×C4×D293 | 2 |
| C22×C22⋊C8 | 293 |