Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×C4×#4223 | C2 | semidirect |
| 3. #13050229 | C2 | direct (N × H) |
| 6. C2×Q8×C41 | C4 | semidirect |
| 9. #10620310 | C4 | semidirect |
| 12. C2×D164 | C4 | semidirect |
| 17. C4×#4223 | C22 | semidirect |
| 19. #10620297 | C22 | semidirect |
| 25. Q8×C41 | C2×C4 | semidirect |
| 32. D164 | C2×C4 | semidirect |
| 52. C2×C41 | #104 | semidirect |
| 58. C41 | C2×#104 | semidirect |
| 67. C2×Q8 | #4223 | semidirect |
| 81. Q8 | C2×#4223 | semidirect |
| 113. C2 | #13050229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10620297 | 2 |
| C2×C4×#4223 | 2 |
| #13050229 | 2 |
| C2×#10620310 | 2 |
| C2×#104 | 41 |