Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #28409837 | C2 | semidirect |
| 2. #28409470 | C2 | semidirect |
| 3. C2×D3632 | C2 | semidirect |
| 4. #28409302 | C2 | semidirect |
| 5. #28408846 | C2 | semidirect |
| 6. #28408840 | C2 | semidirect |
| 7. #350×C227 | C2 | semidirect |
| 16. C2×D1816 | C22 | semidirect |
| 20. #20300224 | C22 | semidirect |
| 23. M32×C227 | C22 | semidirect |
| 24. C2×C16×C227 | C22 | semidirect |
| 93. C227 | #2192 | semidirect |
| 101. #350 | D227 | semidirect |
| 115. M32 | C2×D227 | semidirect |
| 116. C2×C16 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409837 | 2 |
| #28409470 | 2 |
| C2×D3632 | 2 |
| #28409302 | 2 |
| #28408846 | 2 |
| #28408840 | 2 |
| #350×C227 | 2 |
| #2192 | 227 |