Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16812727 | C2 | semidirect |
| 2. #20295576 | C2 | semidirect |
| 3. C2×C4×D436 | C2 | semidirect |
| 4. #20295242 | C2 | semidirect |
| 5. #20295232 | C2 | semidirect |
| 6. #20295222 | C2 | semidirect |
| 7. #20295028 | C2 | semidirect |
| 8. #423×C109 | C2 | semidirect |
| 15. #16812699 | C22 | semidirect |
| 16. #16812696 | C22 | semidirect |
| 17. #16812687 | C22 | semidirect |
| 28. #16812624 | C22 | semidirect |
| 29. #16812621 | C22 | semidirect |
| 32. C4⋊C8×C109 | C22 | semidirect |
| 33. C4⋊C8×C109 | C22 | semidirect |
| 42. C2×D436 | D4 | semidirect |
| 118. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 130. C109 | #3036 | semidirect |
| 137. #423 | D109 | semidirect |
| 160. C4⋊C8 | C2×D109 | semidirect |
| 161. C4⋊C8 | C2×D109 | semidirect |
| 250. C4 | #16812727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812727 | 2 |
| #20295576 | 2 |
| C2×C4×D436 | 2 |
| #20295242 | 2 |
| #20295232 | 2 |
| #20295222 | 2 |
| #20295028 | 2 |
| #423×C109 | 2 |
| #3036 | 109 |