Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813628 | C2 | semidirect |
| 2. #20299176 | C2 | semidirect |
| 3. #20298853 | C2 | semidirect |
| 4. #20298848 | C2 | semidirect |
| 5. #20298824 | C2 | semidirect |
| 6. C2×#16813554 | C2 | semidirect |
| 7. #20298599 | C2 | semidirect |
| 8. C2×#135×C113 | C2 | semidirect |
| 57. C2×C8×C113 | D4 | semidirect |
| 106. C113 | #3060 | semidirect |
| 107. C2×#135 | D113 | semidirect |
| 158. C2×C8 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813628 | 2 |
| #20299176 | 2 |
| #20298853 | 2 |
| #20298848 | 2 |
| #20298824 | 2 |
| C2×#16813554 | 2 |
| #20298599 | 2 |
| C2×#135×C113 | 2 |
| #3060 | 113 |