Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
210 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 50 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. C2×C22⋊#4223 | C2 | semidirect |
| 2. #13050223 | C2 | semidirect |
| 3. #13050222 | C2 | semidirect |
| 5. C23×D41 | C4 | semidirect |
| 8. C2×D4×C41 | C4 | semidirect |
| 9. C2×C22⋊D41 | C4 | semidirect |
| 14. C2×C4×D41 | C4 | semidirect |
| 16. C22⋊#4223 | C22 | semidirect |
| 18. C23×C41 | C2×C4 | semidirect |
| 24. C22×D41 | C2×C4 | semidirect |
| 31. C2×C4×C41 | C2×C4 | semidirect |
| 34. C2×Dic41 | C2×C4 | semidirect |
| 64. D41 | #99 | semidirect |
| 66. C41 | C2×#99 | semidirect |
| 78. C2×D4 | #4223 | semidirect |
| 93. C23 | C2×#4223 | semidirect |
| 103. C2×C4 | C2×#4223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#4223 | 2 |
| #13050223 | 2 |
| #13050222 | 2 |
| C2×D4×D41 | 2 |
| C2×#99 | 41 |