Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16812626 | C2 | semidirect |
| 3. #20295030 | C2 | semidirect |
| 4. #20294927 | C2 | semidirect |
| 5. #20294795 | C2 | semidirect |
| 6. #20294785 | C2 | semidirect |
| 7. #520×C109 | C2 | semidirect |
| 10. #16812724 | C4 | semidirect |
| 34. C2×D436 | C2×C4 | semidirect |
| 41. #13182013 | C2×C4 | semidirect |
| 75. Q8×C109 | C22⋊C4 | semidirect |
| 79. D4×C109 | C22⋊C4 | semidirect |
| 133. C109 | #1883 | semidirect |
| 135. #520 | D109 | semidirect |
| 208. Q8 | #13182006 | semidirect |
| 216. D4 | #13182006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| C2×#16812626 | 2 |
| #20295030 | 2 |
| #20294927 | 2 |
| #20294795 | 2 |
| #20294785 | 2 |
| #520×C109 | 2 |
| #1883 | 109 |