Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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×#20300223 | C2 | semidirect |
| 3. #28409038 | C2 | semidirect |
| 4. #28409037 | C2 | semidirect |
| 5. C2×#20300204 | C2 | semidirect |
| 6. #28408990 | C2 | semidirect |
| 7. C2×#100×C227 | C2 | semidirect |
| 12. C2×#16813869 | C4 | semidirect |
| 111. C227 | #1978 | semidirect |
| 118. C2×#100 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813869 | 2 |
| C2×#20300223 | 2 |
| #28409038 | 2 |
| #28409037 | 2 |
| C2×#20300204 | 2 |
| #28408990 | 2 |
| C2×#100×C227 | 2 |
| #1978 | 227 |