Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C22×#13182018 | C2 | semidirect |
| 2. #20295597 | C2 | semidirect |
| 4. #20295272 | C2 | semidirect |
| 5. #20295255 | C2 | semidirect |
| 6. #20295064 | C2 | semidirect |
| 7. #20295036 | C2 | semidirect |
| 8. #20295032 | C2 | semidirect |
| 9. C2×#131×C109 | C2 | semidirect |
| 20. #16812678 | C22 | semidirect |
| 25. #16812633 | C22 | semidirect |
| 26. #16812631 | C22 | semidirect |
| 27. #16812624 | C22 | semidirect |
| 32. C2×M16×C109 | C22 | semidirect |
| 34. C22×C8×C109 | C22 | semidirect |
| 67. C2×C8×C109 | D4 | semidirect |
| 121. C109 | #3057 | semidirect |
| 123. C2×#131 | D109 | semidirect |
| 139. C2×M16 | C2×D109 | semidirect |
| 141. C22×C8 | C2×D109 | semidirect |
| 179. C2×C8 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182018 | 2 |
| #20295597 | 2 |
| #20295590 | 2 |
| #20295272 | 2 |
| #20295255 | 2 |
| #20295064 | 2 |
| #20295036 | 2 |
| #20295032 | 2 |
| C2×#131×C109 | 2 |
| #3057 | 109 |