Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 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. D4×#4223 | C2 | semidirect |
| 2. #13050243 | C2 | semidirect |
| 3. C2×C22⋊#4223 | C2 | semidirect |
| 6. C22×#4223 | C22 | semidirect |
| 7. C2×D4×C41 | C4 | semidirect |
| 8. C2×C22⋊D41 | C4 | semidirect |
| 9. D4×D41 | C4 | semidirect |
| 11. C2×D164 | C4 | semidirect |
| 14. C22⋊#4223 | C22 | semidirect |
| 15. C4⋊#4223 | C22 | semidirect |
| 16. C4×#4223 | C22 | semidirect |
| 17. C23×C41 | C2×C4 | semidirect |
| 19. C22×D41 | C2×C4 | semidirect |
| 20. C22×D41 | C2×C4 | semidirect |
| 25. D4×C41 | C2×C4 | semidirect |
| 26. C2×C4×C41 | C2×C4 | semidirect |
| 27. C22⋊D41 | C2×C4 | semidirect |
| 28. C2×Dic41 | C2×C4 | semidirect |
| 29. D164 | C2×C4 | semidirect |
| 30. C4×D41 | C2×C4 | semidirect |
| 52. C41 | #518 | semidirect |
| 62. C2×D4 | #4223 | semidirect |
| 74. C23 | C2×#4223 | semidirect |
| 77. D4 | C2×#4223 | semidirect |
| 83. C2×C4 | C2×#4223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#4223 | 2 |
| #13050243 | 2 |
| C2×C22⋊#4223 | 2 |
| C2×D4×D41 | 2 |
| #518 | 41 |