Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20295074 | C2 | semidirect |
| 5. #20294798 | C2 | semidirect |
| 6. #20294786 | C2 | semidirect |
| 7. C4×M16×C109 | C2 | semidirect |
| 16. #16812617 | C4 | semidirect |
| 17. #16812615 | C4 | semidirect |
| 96. C109 | #1932 | semidirect |
| 101. C4×M16 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295074 | 2 |
| #20295042 | 2 |
| C2×#16812627 | 2 |
| #20295008 | 2 |
| #20294798 | 2 |
| #20294786 | 2 |
| C4×M16×C109 | 2 |
| #1932 | 109 |