Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16812726 | C2 | semidirect |
| 2. #20295577 | C2 | semidirect |
| 3. C4×D4×D109 | C2 | semidirect |
| 4. #20295244 | C2 | semidirect |
| 5. #20295243 | C2 | semidirect |
| 6. #20295228 | C2 | semidirect |
| 7. #20295222 | C2 | semidirect |
| 8. #20295221 | C2 | semidirect |
| 9. #20295048 | C2 | semidirect |
| 10. #20295026 | C2 | semidirect |
| 11. #461×C109 | C2 | semidirect |
| 20. #16812696 | C22 | semidirect |
| 21. #16812688 | C22 | semidirect |
| 34. C4⋊#11724784 | C22 | semidirect |
| 35. #16812628 | C22 | semidirect |
| 36. #16812623 | C22 | semidirect |
| 37. #16812621 | C22 | semidirect |
| 38. #16812619 | C22 | semidirect |
| 40. C4⋊Q8×C109 | C22 | semidirect |
| 42. C4⋊C8×C109 | C22 | semidirect |
| 43. #103×C109 | C22 | semidirect |
| 54. D4×D109 | D4 | semidirect |
| 146. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 161. C109 | #3036 | semidirect |
| 168. #461 | D109 | semidirect |
| 182. C4⋊Q8 | C2×D109 | semidirect |
| 200. C4⋊C8 | C2×D109 | semidirect |
| 202. #103 | C2×D109 | semidirect |
| 311. C4 | #16812726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812726 | 2 |
| #20295577 | 2 |
| C4×D4×D109 | 2 |
| #20295244 | 2 |
| #20295243 | 2 |
| #20295228 | 2 |
| #20295222 | 2 |
| #20295221 | 2 |
| #20295048 | 2 |
| #20295026 | 2 |
| #461×C109 | 2 |
| #3036 | 109 |