Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 1. C22×#13182016 | C2 | semidirect |
| 2. C2×#16812706 | C2 | semidirect |
| 4. #20295274 | C2 | semidirect |
| 5. #20295257 | C2 | semidirect |
| 6. #20295062 | C2 | semidirect |
| 7. #20295035 | C2 | semidirect |
| 8. #20295030 | C2 | semidirect |
| 9. #536×C109 | C2 | semidirect |
| 16. C2×#13182013 | C22 | semidirect |
| 18. C22×#11724784 | C22 | semidirect |
| 24. #16812632 | C22 | semidirect |
| 25. #16812630 | C22 | semidirect |
| 26. #16812623 | C22 | semidirect |
| 33. C22⋊Q8×C109 | C22 | semidirect |
| 46. C2×#11724784 | D4 | semidirect |
| 121. C109 | #3057 | semidirect |
| 124. #536 | D109 | semidirect |
| 147. C22⋊Q8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182016 | 2 |
| C2×#16812706 | 2 |
| #20295590 | 2 |
| #20295274 | 2 |
| #20295257 | 2 |
| #20295062 | 2 |
| #20295035 | 2 |
| #20295030 | 2 |
| #536×C109 | 2 |
| #3057 | 109 |