Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
516 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#20300282 | C2 | semidirect |
| 3. #28408927 | C2 | semidirect |
| 4. #28408926 | C2 | semidirect |
| 5. #28408922 | C2 | semidirect |
| 6. C42×Dic227 | C2 | semidirect |
| 7. C2×#126×C227 | C2 | semidirect |
| 39. C42×C227 | D4 | semidirect |
| 74. Dic227 | #126 | semidirect |
| 80. C227 | #2860 | semidirect |
| 83. C2×#126 | D227 | semidirect |
| 120. C42 | C22⋊D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300282 | 2 |
| #28408932 | 2 |
| #28408927 | 2 |
| #28408926 | 2 |
| #28408922 | 2 |
| C42×Dic227 | 2 |
| C2×#126×C227 | 2 |
| #2860 | 227 |