Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #13050159 | C2 | semidirect |
| 2. #13050155 | C2 | semidirect |
| 3. #13050153 | C2 | semidirect |
| 4. #13050149 | C2 | semidirect |
| 5. #13050140 | C2 | semidirect |
| 7. C4×D164 | C2 | semidirect |
| 8. C4×D164 | C2 | semidirect |
| 9. #13050121 | C2 | semidirect |
| 10. C42×D41 | C2 | semidirect |
| 11. C4×Q8×C41 | C2 | semidirect |
| 75. C41 | #529 | semidirect |
| 82. C4×Q8 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050159 | 2 |
| #13050155 | 2 |
| #13050153 | 2 |
| #13050149 | 2 |
| #13050140 | 2 |
| #13050139 | 2 |
| C4×D164 | 2 |
| #13050121 | 2 |
| C42×D41 | 2 |
| C4×Q8×C41 | 2 |
| #529 | 41 |