Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D227 | C2 | semidirect |
| 2. C2×#20300317 | C2 | semidirect |
| 4. #28409190 | C2 | semidirect |
| 5. #28409189 | C2 | semidirect |
| 6. #28409188 | C2 | semidirect |
| 7. #28409170 | C2 | semidirect |
| 8. #28409169 | C2 | semidirect |
| 9. #28409039 | C2 | semidirect |
| 10. #28408994 | C2 | semidirect |
| 11. #448×C227 | C2 | semidirect |
| 23. C2×Dic908 | C22 | semidirect |
| 24. C2×#16813874 | C22 | semidirect |
| 25. C2×#16813872 | C22 | semidirect |
| 35. #20300213 | C22 | semidirect |
| 36. #20300212 | C22 | semidirect |
| 37. #20300211 | C22 | semidirect |
| 41. C2×SD16×C227 | C22 | semidirect |
| 43. #103×C227 | C22 | semidirect |
| 59. Q8×D227 | D4 | semidirect |
| 144. C22×C227 | #137 | semidirect |
| 152. C2×D227 | #137 | semidirect |
| 169. C227 | #3004 | semidirect |
| 179. #448 | D227 | semidirect |
| 197. C2×SD16 | C2×D227 | semidirect |
| 211. #103 | C2×D227 | semidirect |
| 321. C22 | #20300317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D227 | 2 |
| C2×#20300317 | 2 |
| #28409542 | 2 |
| #28409190 | 2 |
| #28409189 | 2 |
| #28409188 | 2 |
| #28409170 | 2 |
| #28409169 | 2 |
| #28409039 | 2 |
| #28408994 | 2 |
| #448×C227 | 2 |
| #3004 | 227 |