Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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. #20296033 | C2 | semidirect |
| 4. C2×#16812753 | C2 | semidirect |
| 5. #20295902 | C2 | semidirect |
| 6. #20295896 | C2 | semidirect |
| 21. #16812624 | C4 | semidirect |
| 22. #16812622 | C4 | semidirect |
| 23. #16812620 | C4 | semidirect |
| 24. #102×C109 | C4 | semidirect |
| 106. C109 | #1938 | semidirect |
| 127. #102 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296033 | 2 |
| C2×#16812763 | 2 |
| #20296000 | 2 |
| C2×#16812753 | 2 |
| #20295902 | 2 |
| #20295896 | 2 |
| #20295019 | 2 |
| #1938 | 109 |