Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20295500 | C2 | semidirect |
| 3. #20295136 | C2 | semidirect |
| 4. C4×#13182014 | C2 | semidirect |
| 5. #20295062 | C2 | semidirect |
| 6. #20295031 | C2 | semidirect |
| 7. #20295030 | C2 | semidirect |
| 8. #20294982 | C2 | semidirect |
| 9. #518×C109 | C2 | semidirect |
| 11. C2×#13182014 | C4 | semidirect |
| 16. C4×D436 | C22 | semidirect |
| 20. #16812632 | C22 | semidirect |
| 21. #16812630 | C22 | semidirect |
| 22. #16812620 | C22 | semidirect |
| 23. #16812619 | C22 | semidirect |
| 24. #16812610 | C22 | semidirect |
| 25. C4×#11724784 | C22 | semidirect |
| 28. C4×D4×C109 | C22 | semidirect |
| 35. C2×D436 | C2×C4 | semidirect |
| 38. #13182014 | C2×C4 | semidirect |
| 39. #13182014 | C2×C4 | semidirect |
| 41. C2×#11724784 | C2×C4 | semidirect |
| 52. C2×D4×C109 | C2×C4 | semidirect |
| 109. C109 | #2948 | semidirect |
| 112. #518 | D109 | semidirect |
| 129. C4×D4 | C2×D109 | semidirect |
| 149. C2×D4 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182014 | 2 |
| #20295500 | 2 |
| #20295136 | 2 |
| C4×#13182014 | 2 |
| #20295062 | 2 |
| #20295031 | 2 |
| #20295030 | 2 |
| #20294982 | 2 |
| #518×C109 | 2 |
| #2948 | 109 |