Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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×#20296329 | C2 | semidirect |
| 2. #28380763 | C2 | direct (N × H) |
| 3. C2×#20296319 | C2 | semidirect |
| 4. C2×#20296317 | C2 | semidirect |
| 5. C2×#20296316 | C2 | semidirect |
| 6. C2×#20296314 | C2 | semidirect |
| 7. C22×C439⋊C8 | C2 | semidirect |
| 8. C2×#41×C439 | C2 | semidirect |
| 10. #20296329 | C22 | semidirect |
| 15. #20296319 | C22 | semidirect |
| 16. #20296317 | C22 | semidirect |
| 17. #20296316 | C22 | semidirect |
| 18. #20296314 | C22 | semidirect |
| 21. C2×C439⋊C8 | C22 | semidirect |
| 23. #41×C439 | C22 | semidirect |
| 66. C2×C439 | #135 | semidirect |
| 69. C439 | C2×#135 | semidirect |
| 72. C2×#41 | D439 | semidirect |
| 82. #41 | C2×D439 | semidirect |
| 137. C2 | #28380763 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296329 | 2 |
| #28380763 | 2 |
| C2×#20296319 | 2 |
| C2×#20296317 | 2 |
| C2×#20296316 | 2 |
| C2×#20296314 | 2 |
| C22×C439⋊C8 | 2 |
| C2×#41×C439 | 2 |
| C2×#135 | 439 |