Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
374 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16812623 | C2 | semidirect |
| 5. #20294788 | C2 | semidirect |
| 6. #20294781 | C2 | semidirect |
| 7. C2×C4×Q8×C109 | C2 | semidirect |
| 11. C2×#13182016 | C4 | semidirect |
| 73. Q8×C109 | C22⋊C4 | semidirect |
| 85. C2×C4×C109 | SD16 | semidirect |
| 133. C109 | #1880 | semidirect |
| 135. C2×C4×Q8 | D109 | semidirect |
| 206. Q8 | #13182006 | semidirect |
| 225. C2×C4 | #13182016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182016 | 2 |
| C2×#16812623 | 2 |
| C2×#16812619 | 2 |
| #20294928 | 2 |
| #20294788 | 2 |
| #20294781 | 2 |
| C2×C4×Q8×C109 | 2 |
| #1880 | 109 |