Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28410600 | C2 | semidirect |
| 2. #28410599 | C2 | semidirect |
| 3. #28410585 | C2 | semidirect |
| 4. #28410584 | C2 | semidirect |
| 5. #28410581 | C2 | semidirect |
| 6. #28410573 | C2 | semidirect |
| 7. #28410572 | C2 | semidirect |
| 8. C2×#20300731 | C2 | semidirect |
| 9. Q16×D457 | C2 | semidirect |
| 10. #28410560 | C2 | semidirect |
| 11. #137×C457 | C2 | semidirect |
| 87. C457 | #578 | semidirect |
| 94. #137 | D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410600 | 2 |
| #28410599 | 2 |
| #28410585 | 2 |
| #28410584 | 2 |
| #28410581 | 2 |
| #28410573 | 2 |
| #28410572 | 2 |
| C2×#20300731 | 2 |
| Q16×D457 | 2 |
| #28410560 | 2 |
| #137×C457 | 2 |
| #578 | 457 |