Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20300336 | C2 | semidirect |
| 2. C2×#20300314 | C2 | semidirect |
| 3. #28409599 | C2 | semidirect |
| 4. #28409176 | C2 | semidirect |
| 5. #28409169 | C2 | semidirect |
| 6. #28409041 | C2 | semidirect |
| 7. #28409029 | C2 | semidirect |
| 8. #28408998 | C2 | semidirect |
| 9. C22×SD16×C227 | C2 | semidirect |
| 13. C2×#16813885 | C22 | semidirect |
| 18. C2×Q8×D227 | C22 | semidirect |
| 28. #20300213 | C22 | semidirect |
| 29. #20300212 | C22 | semidirect |
| 30. #20300210 | C22 | semidirect |
| 31. (C2×D227)⋊C8 | C22 | semidirect |
| 44. #16813884 | D4 | semidirect |
| 72. C2×Q8×C227 | D4 | semidirect |
| 145. C227 | #3010 | semidirect |
| 149. C22×SD16 | D227 | semidirect |
| 200. C2×Q8 | C22⋊D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300336 | 2 |
| C2×#20300314 | 2 |
| #28409599 | 2 |
| #28409176 | 2 |
| #28409169 | 2 |
| #28409041 | 2 |
| #28409029 | 2 |
| #28408998 | 2 |
| C22×SD16×C227 | 2 |
| #3010 | 227 |