Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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×#10620297 | C2 | semidirect |
| 2. #13050243 | C2 | semidirect |
| 3. #13050229 | C2 | semidirect |
| 4. #13050228 | C2 | semidirect |
| 6. #41×C41 | C4 | semidirect |
| 8. Q8×D41 | C4 | semidirect |
| 12. D4×D41 | C4 | semidirect |
| 14. #10620306 | C4 | semidirect |
| 20. C4×#4223 | C22 | semidirect |
| 22. #10620297 | C22 | semidirect |
| 69. C41 | #421 | semidirect |
| 80. #41 | #4223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620297 | 2 |
| #13050243 | 2 |
| #13050229 | 2 |
| #13050228 | 2 |
| #41×D41 | 2 |
| #421 | 41 |