Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20295323 | C2 | semidirect |
| 3. #20295323 | C2 | semidirect |
| 4. #20295313 | C2 | semidirect |
| 5. #20295303 | C2 | semidirect |
| 6. #20295066 | C2 | semidirect |
| 7. #20295062 | C2 | semidirect |
| 8. #20295053 | C2 | semidirect |
| 11. #544×C109 | C2 | 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 |
| 34. C4⋊Q8×C109 | C22 | semidirect |
| 36. #125×C109 | C22 | semidirect |
| 44. C2×D436 | Q8 | semidirect |
| 125. C109 | #3081 | semidirect |
| 126. #544 | D109 | semidirect |
| 141. C4⋊Q8 | C2×D109 | semidirect |
| 143. #125 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295500 | 2 |
| #20295323 | 2 |
| #20295313 | 2 |
| #20295303 | 2 |
| #20295066 | 2 |
| #20295062 | 2 |
| #20295053 | 2 |
| #20295030 | 2 |
| C2×#16812619 | 2 |
| #544×C109 | 2 |
| #3081 | 109 |