Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 2. #20294821 | C2 | semidirect |
| 8. C22×Q8×C109 | C4 | semidirect |
| 9. C4⋊Q8×C109 | C4 | semidirect |
| 13. #117×C109 | C4 | semidirect |
| 65. C109 | #2129 | semidirect |
| 70. C22×Q8 | Dic109 | semidirect |
| 71. C4⋊Q8 | Dic109 | semidirect |
| 76. #117 | Dic109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295000 | 2 |
| #20294821 | 2 |
| #536×C109 | 2 |
| #2129 | 109 |