Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#16813872 | C2 | semidirect |
| 2. C2×#16813868 | C2 | semidirect |
| 3. #20300267 | C2 | semidirect |
| 4. #20300221 | C2 | semidirect |
| 5. #20300211 | C2 | semidirect |
| 6. #20300209 | C2 | semidirect |
| 26. C227⋊C8 | D4 | semidirect |
| 55. C227 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813872 | 2 |
| C2×#16813868 | 2 |
| #20300267 | 2 |
| #20300221 | 2 |
| #20300211 | 2 |
| #20300209 | 2 |
| #121×C227 | 2 |
| #468 | 227 |