Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
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×#20297746 | C2 | semidirect |
| 2. C2×C4×#14267798 | C2 | semidirect |
| 3. #28385405 | C2 | direct (N × H) |
| 7. #20297746 | C22 | semidirect |
| 10. C4×#14267798 | C22 | semidirect |
| 13. #20297737 | C4 | semidirect |
| 16. C2×D1796 | C4 | semidirect |
| 19. C2×Q8×C449 | C4 | semidirect |
| 28. D1796 | C2×C4 | semidirect |
| 37. Q8×C449 | C2×C4 | semidirect |
| 52. C2×C449 | #104 | semidirect |
| 57. C449 | C2×#104 | semidirect |
| 67. C2×Q8 | #14267798 | semidirect |
| 81. Q8 | C2×#14267798 | semidirect |
| 113. C2 | #28385405 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20297746 | 2 |
| C2×C4×#14267798 | 2 |
| #28385405 | 2 |
| C2×#20297737 | 2 |
| C2×#104 | 449 |