Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C23×Dic449 | C2 | semidirect |
| 3. C2×#20297713 | C2 | semidirect |
| 4. #28385247 | C2 | semidirect |
| 5. C2×C22⋊C4×C449 | C2 | semidirect |
| 9. C2×C22⋊D449 | C4 | semidirect |
| 22. C22×D449 | C2×C4 | semidirect |
| 29. C2×Dic449 | C2×C4 | semidirect |
| 30. C2×Dic449 | D4 | semidirect |
| 44. C22×C449 | C22⋊C4 | semidirect |
| 65. C449 | #386 | semidirect |
| 70. C2×C22⋊C4 | D449 | semidirect |
| 115. C22 | #20297713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D449 | 2 |
| C23×Dic449 | 2 |
| C2×#20297713 | 2 |
| #28385247 | 2 |
| C2×C22⋊C4×C449 | 2 |
| #386 | 449 |