Finite Group DatabasebetaFinite Group DatabasebetaOrder 28736.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×C8×D449 | C2 | semidirect |
| 3. #28385298 | C2 | semidirect |
| 4. #28385264 | C2 | semidirect |
| 5. #28385262 | C2 | semidirect |
| 6. #28385260 | C2 | semidirect |
| 7. #103×C449 | C2 | semidirect |
| 9. #20297737 | C4 | semidirect |
| 57. C449 | #416 | semidirect |
| 63. #103 | D449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20297737 | 2 |
| C2×C8×D449 | 2 |
| #28385298 | 2 |
| #28385264 | 2 |
| #28385262 | 2 |
| #28385260 | 2 |
| #103×C449 | 2 |
| #416 | 449 |