Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16812690 | C2 | semidirect |
| 3. #20295336 | C2 | semidirect |
| 4. #20295332 | C2 | semidirect |
| 5. #20295329 | C2 | semidirect |
| 6. #20295325 | C2 | semidirect |
| 7. #20295069 | C2 | semidirect |
| 8. #20295049 | C2 | semidirect |
| 11. #428×C109 | C2 | semidirect |
| 136. C109 | #3080 | semidirect |
| 144. #428 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812690 | 2 |
| #20295494 | 2 |
| #20295336 | 2 |
| #20295332 | 2 |
| #20295329 | 2 |
| #20295325 | 2 |
| #20295069 | 2 |
| #20295049 | 2 |
| #20295028 | 2 |
| #20295025 | 2 |
| #428×C109 | 2 |
| #3080 | 109 |