Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #28409317 | C2 | semidirect |
| 3. Q8×C227⋊C8 | C2 | semidirect |
| 4. #28408782 | C2 | semidirect |
| 5. #28408777 | C2 | semidirect |
| 48. C227⋊C8 | SD16 | semidirect |
| 51. Q8×C227 | SD16 | semidirect |
| 79. C227 | #1666 | semidirect |
| 126. Q8 | #16813872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409404 | 2 |
| #28409317 | 2 |
| Q8×C227⋊C8 | 2 |
| #28408782 | 2 |
| #28408777 | 2 |
| #28408776 | 2 |
| #460×C227 | 2 |
| #1666 | 227 |