Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20295654 | C2 | semidirect |
| 2. #20295326 | C2 | semidirect |
| 3. #20295326 | C2 | semidirect |
| 4. #20295316 | C2 | semidirect |
| 5. #20295306 | C2 | semidirect |
| 6. #20295069 | C2 | semidirect |
| 7. #20295062 | C2 | semidirect |
| 8. #20295053 | C2 | semidirect |
| 14. #16812699 | C22 | semidirect |
| 16. #16812691 | C22 | semidirect |
| 21. #16812632 | C22 | semidirect |
| 22. #16812632 | C22 | semidirect |
| 23. #16812632 | C22 | semidirect |
| 24. #16812630 | C22 | semidirect |
| 25. #16812630 | C22 | semidirect |
| 26. #16812630 | C22 | semidirect |
| 27. C4⋊#11724784 | C22 | semidirect |
| 28. C4⋊#11724784 | C22 | semidirect |
| 60. C2×D4×C109 | Q8 | semidirect |
| 125. C109 | #3081 | semidirect |
| 170. C2×D4 | Dic218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295654 | 2 |
| #20295326 | 2 |
| #20295316 | 2 |
| #20295306 | 2 |
| #20295069 | 2 |
| #20295062 | 2 |
| #20295053 | 2 |
| #20295031 | 2 |
| C2×#16812620 | 2 |
| #518×C109 | 2 |
| #3081 | 109 |