Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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. #20296037 | C2 | semidirect |
| 4. #20295992 | C2 | semidirect |
| 5. #20295905 | C2 | semidirect |
| 6. #20295901 | C2 | semidirect |
| 23. #16812616 | C4 | semidirect |
| 24. #16812615 | C4 | semidirect |
| 25. #16812615 | C4 | semidirect |
| 26. #100×C109 | C4 | semidirect |
| 115. C109 | #1931 | semidirect |
| 139. #100 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296037 | 2 |
| #20296018 | 2 |
| C2×#16812761 | 2 |
| #20295992 | 2 |
| #20295905 | 2 |
| #20295901 | 2 |
| #100×D109 | 2 |
| #1931 | 109 |