Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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×#20300203 | C2 | semidirect |
| 3. C2×#20300202 | C2 | semidirect |
| 4. C2×#20300202 | C2 | semidirect |
| 5. #28408890 | C2 | semidirect |
| 6. C22⋊C4×Dic227 | C2 | semidirect |
| 7. C2×#99×C227 | C2 | semidirect |
| 8. C22×C22⋊D227 | C4 | semidirect |
| 16. C2×Dic227⋊C4 | C4 | semidirect |
| 17. C2×C22⋊Dic227 | C4 | semidirect |
| 20. C2×(C2×D227)⋊C4 | C4 | semidirect |
| 59. C22⋊Dic227 | D4 | semidirect |
| 77. C22⋊C4×C227 | D4 | semidirect |
| 171. Dic227 | #99 | semidirect |
| 183. C227 | #1964 | semidirect |
| 189. C2×#99 | D227 | semidirect |
| 260. C22⋊C4 | C22⋊D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300260 | 2 |
| C2×#20300203 | 2 |
| C2×#20300202 | 2 |
| #28408890 | 2 |
| C22⋊C4×Dic227 | 2 |
| C2×#99×C227 | 2 |
| #1964 | 227 |