Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #20295890 | C2 | semidirect |
| 4. #20295889 | C2 | semidirect |
| 5. #20295888 | C2 | semidirect |
| 6. #20295887 | C2 | semidirect |
| 58. C8×C109 | M16 | semidirect |
| 60. #11724784 | M16 | semidirect |
| 78. C109 | #1569 | semidirect |
| 138. C8 | #13182038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296047 | 2 |
| #20296029 | 2 |
| #20295890 | 2 |
| #20295889 | 2 |
| #20295888 | 2 |
| #20295887 | 2 |
| M16×Dic109 | 2 |
| #1569 | 109 |