Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #20294779 | C2 | semidirect |
| 5. #20294778 | C2 | semidirect |
| 6. #20294776 | C2 | semidirect |
| 7. #334×C109 | C2 | semidirect |
| 27. #13182012 | C8 | semidirect |
| 56. C8×C109 | C2×C8 | semidirect |
| 60. #11724784 | C2×C8 | semidirect |
| 78. C109 | #1565 | semidirect |
| 85. #334 | D109 | semidirect |
| 138. C8 | C8×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295078 | 2 |
| C4⋊C8×D109 | 2 |
| C4×#13182012 | 2 |
| #20294779 | 2 |
| #20294778 | 2 |
| #20294776 | 2 |
| #334×C109 | 2 |
| #1565 | 109 |