Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
340 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16812633 | C2 | semidirect |
| 3. C2×#16812624 | C2 | semidirect |
| 5. #20294932 | C2 | semidirect |
| 7. C2×#97×C109 | C2 | semidirect |
| 12. C2×#13182018 | C4 | semidirect |
| 87. C8×C109 | C22⋊C4 | semidirect |
| 113. C109 | #1973 | semidirect |
| 118. C2×#97 | D109 | semidirect |
| 200. C8 | #13182006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182018 | 2 |
| C2×#16812633 | 2 |
| C2×#16812624 | 2 |
| C2×#16812621 | 2 |
| #20294932 | 2 |
| #20294928 | 2 |
| C2×#97×C109 | 2 |
| #1973 | 109 |