Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812721 | C2 | semidirect |
| 2. #20295456 | C2 | direct (N × H) |
| 3. C2×#16812645 | C2 | semidirect |
| 4. C2×#16812643 | C2 | semidirect |
| 5. C2×#16812642 | C2 | semidirect |
| 6. C2×#16812640 | C2 | semidirect |
| 7. C22×#13182004 | C2 | semidirect |
| 8. C2×#135×C109 | C2 | semidirect |
| 11. #16812721 | C22 | semidirect |
| 15. #16812645 | C22 | semidirect |
| 16. #16812643 | C22 | semidirect |
| 17. #16812642 | C22 | semidirect |
| 18. #16812640 | C22 | semidirect |
| 21. C2×#13182004 | C22 | semidirect |
| 24. #135×C109 | C22 | semidirect |
| 96. C2×C109 | #508 | semidirect |
| 100. C109 | C2×#508 | semidirect |
| 102. C2×#135 | D109 | semidirect |
| 114. #135 | C2×D109 | semidirect |
| 197. C2 | #20295456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812721 | 2 |
| #20295456 | 2 |
| C2×#16812645 | 2 |
| C2×#16812643 | 2 |
| C2×#16812642 | 2 |
| C2×#16812640 | 2 |
| C22×#13182004 | 2 |
| C2×#135×C109 | 2 |
| C2×#508 | 109 |