Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 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. C2×#16812730 | C2 | semidirect |
| 2. C22×#13182016 | C2 | semidirect |
| 4. #20295248 | C2 | semidirect |
| 5. #20295226 | C2 | semidirect |
| 6. #20295053 | C2 | semidirect |
| 7. #20295030 | C2 | semidirect |
| 8. #20295020 | C2 | semidirect |
| 9. #519×C109 | C2 | semidirect |
| 13. C2×#13182019 | C22 | semidirect |
| 16. C2×#13182016 | C22 | semidirect |
| 23. C4⋊#11724784 | C22 | semidirect |
| 24. #16812622 | C22 | semidirect |
| 26. #16812619 | C22 | semidirect |
| 29. C4×Q8×C109 | C22 | semidirect |
| 55. C2×Q8×C109 | D4 | semidirect |
| 117. C109 | #3043 | semidirect |
| 121. #519 | D109 | semidirect |
| 142. C4×Q8 | C2×D109 | semidirect |
| 156. C2×Q8 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| C22×#13182016 | 2 |
| #20295595 | 2 |
| #20295248 | 2 |
| #20295226 | 2 |
| #20295053 | 2 |
| #20295030 | 2 |
| #20295020 | 2 |
| #519×C109 | 2 |
| #3043 | 109 |