Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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. C2×#16812721 | C2 | semidirect |
| 2. C22×#13182012 | C2 | semidirect |
| 3. #20295538 | C2 | semidirect |
| 4. #20295285 | C2 | semidirect |
| 5. #20295280 | C2 | semidirect |
| 6. #20295273 | C2 | semidirect |
| 7. #20295020 | C2 | semidirect |
| 8. #427×C109 | C2 | semidirect |
| 12. C2×Dic436 | C22 | semidirect |
| 13. C2×#13182018 | C22 | semidirect |
| 14. C2×D872 | C22 | semidirect |
| 24. #16812622 | C22 | semidirect |
| 25. #16812619 | C22 | semidirect |
| 28. #107×C109 | C22 | semidirect |
| 29. #106×C109 | C22 | semidirect |
| 54. C2×C8×C109 | D4 | semidirect |
| 106. C109 | #3054 | semidirect |
| 113. #427 | D109 | semidirect |
| 132. #107 | C2×D109 | semidirect |
| 133. #106 | C2×D109 | semidirect |
| 157. C2×C8 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812721 | 2 |
| C22×#13182012 | 2 |
| #20295538 | 2 |
| #20295285 | 2 |
| #20295280 | 2 |
| #20295273 | 2 |
| #20295020 | 2 |
| #427×C109 | 2 |
| #3054 | 109 |