Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 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. D41⋊M16 | C2 | semidirect |
| 2. C2×C4×#4223 | C2 | semidirect |
| 3. #13050229 | C2 | semidirect |
| 4. #13050228 | C2 | semidirect |
| 7. #41×C41 | C4 | semidirect |
| 9. Q8×D41 | C4 | semidirect |
| 13. D4×D41 | C4 | semidirect |
| 15. #10620306 | C4 | semidirect |
| 20. C4×#4223 | C22 | semidirect |
| 21. #10620297 | C22 | semidirect |
| 27. Q8×C41 | C2×C4 | semidirect |
| 29. D4×C41 | C2×C4 | semidirect |
| 38. D164 | C2×C4 | semidirect |
| 47. Dic82 | C2×C4 | semidirect |
| 68. D41 | #104 | semidirect |
| 70. C41 | C2×#104 | semidirect |
| 81. #41 | #4223 | semidirect |
| 97. Q8 | C2×#4223 | semidirect |
| 104. D4 | C2×#4223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D41⋊M16 | 2 |
| C2×C4×#4223 | 2 |
| #13050229 | 2 |
| #13050228 | 2 |
| #41×D41 | 2 |
| C2×#104 | 41 |