Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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. #28385316 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic449 | C2 | semidirect |
| 4. C2×#20297715 | C2 | semidirect |
| 6. C22×Q8×C449 | C2 | semidirect |
| 12. C4⋊Dic449 | C22 | semidirect |
| 13. #20297715 | C22 | semidirect |
| 16. C2×Q8×C449 | C22 | semidirect |
| 21. C22×D449 | Q8 | semidirect |
| 41. C2×D449 | C2×Q8 | semidirect |
| 46. C2×C449 | C22⋊Q8 | semidirect |
| 51. C449 | C2×C22⋊Q8 | semidirect |
| 53. C22×Q8 | D449 | semidirect |
| 61. C2×Q8 | C2×D449 | semidirect |
| 99. C2 | #28385316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D449 | 2 |
| #28385316 | 2 |
| C2×C4⋊Dic449 | 2 |
| C2×#20297715 | 2 |
| C2×#20297713 | 2 |
| C22×Q8×C449 | 2 |
| C2×C22⋊Q8 | 449 |