Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 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. #13050243 | C2 | direct (N × H) |
| 2. C2×C4⋊#4223 | C2 | semidirect |
| 4. C2×C4×#4223 | C2 | semidirect |
| 8. C22×C4×C41 | C4 | semidirect |
| 9. C22×Dic41 | C4 | semidirect |
| 10. C2×C4×D41 | C4 | semidirect |
| 11. C2×C4×D41 | C4 | semidirect |
| 12. C2×C4×D41 | C4 | semidirect |
| 17. C4⋊#4223 | C22 | semidirect |
| 18. C4×#4223 | C22 | semidirect |
| 29. C2×C4×C41 | C2×C4 | semidirect |
| 32. C2×Dic41 | C2×C4 | semidirect |
| 35. C4×D41 | C2×C4 | semidirect |
| 36. C4×D41 | C2×C4 | semidirect |
| 55. C2×C41 | #117 | semidirect |
| 58. D41 | #117 | semidirect |
| 61. C41 | C2×#117 | semidirect |
| 76. C22×C4 | #4223 | semidirect |
| 99. C2×C4 | C2×#4223 | semidirect |
| 119. C2 | #13050243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050243 | 2 |
| C2×C4⋊#4223 | 2 |
| C2×C22⋊#4223 | 2 |
| C2×C4×#4223 | 2 |
| C22×C4×D41 | 2 |
| C2×#117 | 41 |