Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#16812732 | C2 | semidirect |
| 3. C2×#16812678 | C2 | semidirect |
| 4. #20295190 | C2 | semidirect |
| 5. #20295184 | C2 | semidirect |
| 6. #20295179 | C2 | semidirect |
| 7. #20295028 | C2 | semidirect |
| 8. #407×C109 | C2 | semidirect |
| 15. C22×Dic218 | C22 | semidirect |
| 20. C2×Dic436 | C22 | semidirect |
| 21. C2×#13182018 | C22 | semidirect |
| 25. #16812678 | C22 | semidirect |
| 26. C2×C4⋊Dic109 | C22 | semidirect |
| 29. #16812624 | C22 | semidirect |
| 30. #16812621 | C22 | semidirect |
| 32. C2×M16×C109 | C22 | semidirect |
| 34. C22⋊C8×C109 | C22 | semidirect |
| 126. C22×C109 | #137 | semidirect |
| 147. C109 | #3007 | semidirect |
| 155. #407 | D109 | semidirect |
| 170. C2×M16 | C2×D109 | semidirect |
| 181. C22⋊C8 | C2×D109 | semidirect |
| 277. C22 | #16812732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182029 | 2 |
| C2×#16812732 | 2 |
| C2×#16812678 | 2 |
| #20295190 | 2 |
| #20295184 | 2 |
| #20295179 | 2 |
| #20295028 | 2 |
| #407×C109 | 2 |
| #3007 | 109 |