Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20294926 | C2 | semidirect |
| 3. #20294916 | C2 | semidirect |
| 4. #20294911 | C2 | semidirect |
| 5. #20294904 | C2 | semidirect |
| 6. #20294902 | C2 | semidirect |
| 7. #20294897 | C2 | semidirect |
| 8. #20294889 | C2 | semidirect |
| 9. #380×C109 | C2 | semidirect |
| 13. #16812673 | C4 | semidirect |
| 37. C2×C22⋊D109 | C2×C4 | semidirect |
| 44. C4⋊Dic109 | C2×C4 | semidirect |
| 50. #13182006 | C2×C4 | semidirect |
| 54. C22×C4×C109 | C2×C4 | semidirect |
| 130. C109 | #2377 | semidirect |
| 139. #380 | D109 | semidirect |
| 176. C22×C4 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812673 | 2 |
| #20294926 | 2 |
| #20294916 | 2 |
| #20294911 | 2 |
| #20294904 | 2 |
| #20294902 | 2 |
| #20294897 | 2 |
| #20294889 | 2 |
| #380×C109 | 2 |
| #2377 | 109 |