Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16812698 | C2 | semidirect |
| 3. #20295320 | C2 | semidirect |
| 4. #20295315 | C2 | semidirect |
| 5. #20295310 | C2 | semidirect |
| 6. #20295305 | C2 | semidirect |
| 7. #20295069 | C2 | semidirect |
| 8. #20295049 | C2 | semidirect |
| 11. #428×C109 | C2 | semidirect |
| 44. #13182029 | Q8 | semidirect |
| 104. D436 | C2×Q8 | semidirect |
| 111. Dic218 | C2×Q8 | semidirect |
| 139. C109 | #3079 | semidirect |
| 147. #428 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812698 | 2 |
| #20295494 | 2 |
| #20295320 | 2 |
| #20295315 | 2 |
| #20295310 | 2 |
| #20295305 | 2 |
| #20295069 | 2 |
| #20295049 | 2 |
| #20295028 | 2 |
| #20295025 | 2 |
| #428×C109 | 2 |
| #3079 | 109 |