Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20295632 | C2 | direct (N × H) |
| 2. C2×#16812696 | C2 | semidirect |
| 3. C2×#16812684 | C2 | semidirect |
| 4. C2×#16812674 | C2 | semidirect |
| 5. C2×#16812674 | C2 | semidirect |
| 6. C2×#16812661 | C2 | semidirect |
| 7. C2×#16812656 | C2 | semidirect |
| 8. C2×#125×C109 | C2 | semidirect |
| 14. #16812696 | C22 | semidirect |
| 15. #16812684 | C22 | semidirect |
| 16. #16812674 | C22 | semidirect |
| 17. #16812674 | C22 | semidirect |
| 18. #16812661 | C22 | semidirect |
| 19. #16812656 | C22 | semidirect |
| 25. #125×C109 | C22 | semidirect |
| 92. C2×C109 | #540 | semidirect |
| 98. C109 | C2×#540 | semidirect |
| 101. C2×#125 | D109 | semidirect |
| 113. #125 | C2×D109 | semidirect |
| 192. C2 | #20295632 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295632 | 2 |
| C2×#16812696 | 2 |
| C2×#16812684 | 2 |
| C2×#16812674 | 2 |
| C2×#16812661 | 2 |
| C2×#16812656 | 2 |
| C2×#125×C109 | 2 |
| C2×#540 | 109 |