Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 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. #20299403 | C2 | semidirect |
| 2. #20299039 | C2 | semidirect |
| 3. #20299033 | C2 | semidirect |
| 4. #20299028 | C2 | semidirect |
| 5. C2×#16813565 | C2 | semidirect |
| 6. #20299015 | C2 | semidirect |
| 7. #578×C113 | C2 | semidirect |
| 12. #16813568 | C22 | semidirect |
| 13. #16813566 | C22 | semidirect |
| 14. #16813565 | C22 | semidirect |
| 15. #16813565 | C22 | semidirect |
| 16. #16813563 | C22 | semidirect |
| 17. #16813562 | C22 | semidirect |
| 18. C2×#14268622 | C22 | semidirect |
| 21. #135×C113 | C22 | semidirect |
| 22. C2×Q16×C113 | C22 | semidirect |
| 75. C113 | #3416 | semidirect |
| 76. #578 | D113 | semidirect |
| 88. #135 | C2×D113 | semidirect |
| 89. C2×Q16 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299403 | 2 |
| #20299039 | 2 |
| #20299033 | 2 |
| #20299028 | 2 |
| C2×#16813565 | 2 |
| #20299015 | 2 |
| #578×C113 | 2 |
| #3416 | 113 |