Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×#20300286 | C2 | semidirect |
| 4. #28408939 | C2 | semidirect |
| 5. #28408937 | C2 | semidirect |
| 6. #28408927 | C2 | semidirect |
| 7. #28408901 | C2 | semidirect |
| 36. C22×Dic227 | Q8 | semidirect |
| 99. C22×C227 | C4⋊Q8 | semidirect |
| 112. Dic227 | C22⋊Q8 | semidirect |
| 119. C227 | #2857 | semidirect |
| 219. C22 | #20300286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300286 | 2 |
| C2×#20300267 | 2 |
| C22×C4×Dic227 | 2 |
| #28408939 | 2 |
| #28408937 | 2 |
| #28408927 | 2 |
| #28408901 | 2 |
| #28408890 | 2 |
| C2×C22⋊Q8×C227 | 2 |
| #2857 | 227 |