Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 2. #20295318 | C2 | semidirect |
| 3. #20295313 | C2 | semidirect |
| 4. #20295308 | C2 | semidirect |
| 5. #20295303 | C2 | semidirect |
| 6. #20295066 | C2 | semidirect |
| 7. #20295050 | C2 | semidirect |
| 9. C2×C4⋊Q8×C109 | C2 | semidirect |
| 36. #13182029 | Q8 | semidirect |
| 91. D436 | C2×Q8 | semidirect |
| 96. Dic218 | C2×Q8 | semidirect |
| 122. C109 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13182029 | 2 |
| #20295318 | 2 |
| #20295313 | 2 |
| #20295308 | 2 |
| #20295303 | 2 |
| #20295066 | 2 |
| #20295050 | 2 |
| #20295025 | 2 |
| C2×C4⋊Q8×C109 | 2 |
| #3079 | 109 |