Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20299415 | C2 | semidirect |
| 2. #20299039 | C2 | semidirect |
| 3. #20299038 | C2 | semidirect |
| 4. #20299028 | C2 | semidirect |
| 5. C2×#16813568 | C2 | semidirect |
| 6. #20299015 | C2 | semidirect |
| 7. #578×C113 | C2 | semidirect |
| 74. C113 | #3417 | semidirect |
| 76. #578 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299415 | 2 |
| #20299039 | 2 |
| #20299038 | 2 |
| #20299028 | 2 |
| C2×#16813568 | 2 |
| #20299015 | 2 |
| #578×C113 | 2 |
| #3417 | 113 |