Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. #20295792 | C2 | semidirect |
| 3. #20295147 | C2 | semidirect |
| 4. #20295142 | C2 | semidirect |
| 5. C2×#16812625 | C2 | semidirect |
| 6. M16×Dic109 | C2 | semidirect |
| 7. #430×C109 | C2 | semidirect |
| 9. #16812732 | C4 | semidirect |
| 10. #16812727 | C4 | semidirect |
| 12. #16812707 | C22 | semidirect |
| 17. #16812625 | C22 | semidirect |
| 18. #16812625 | C22 | semidirect |
| 19. #16812609 | C22 | semidirect |
| 20. C8×Dic109 | C22 | semidirect |
| 23. #108×C109 | C22 | semidirect |
| 33. Dic436 | C2×C4 | semidirect |
| 34. #13182018 | C2×C4 | semidirect |
| 35. D872 | C2×C4 | semidirect |
| 86. C109 | #2956 | semidirect |
| 91. #430 | D109 | semidirect |
| 105. #108 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295826 | 2 |
| #20295792 | 2 |
| #20295147 | 2 |
| #20295142 | 2 |
| C2×#16812625 | 2 |
| M16×Dic109 | 2 |
| #430×C109 | 2 |
| #2956 | 109 |