Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 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×#16812726 | C2 | semidirect |
| 2. #20295577 | C2 | semidirect |
| 3. #127×D109 | C2 | semidirect |
| 4. #20295412 | C2 | semidirect |
| 5. #20295403 | C2 | semidirect |
| 6. #20295402 | C2 | semidirect |
| 7. #20295400 | C2 | semidirect |
| 8. C4×#13182012 | C2 | semidirect |
| 9. #492×C109 | C2 | semidirect |
| 14. C2×#13182016 | C22 | semidirect |
| 15. C2×D872 | C22 | semidirect |
| 16. C2×#13182014 | C22 | semidirect |
| 19. #16812696 | C22 | semidirect |
| 22. #16812688 | C22 | semidirect |
| 26. #16812609 | C22 | semidirect |
| 27. C4×#11724784 | C22 | semidirect |
| 28. C2×SD16×C109 | C22 | semidirect |
| 29. C4⋊Q8×C109 | C22 | semidirect |
| 31. C4×C8×C109 | C22 | semidirect |
| 49. #13182012 | D4 | semidirect |
| 85. C8×C109 | C2×D4 | semidirect |
| 86. #11724784 | C2×D4 | semidirect |
| 98. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 109. C109 | #3151 | semidirect |
| 117. #492 | D109 | semidirect |
| 124. C2×SD16 | C2×D109 | semidirect |
| 128. C4⋊Q8 | C2×D109 | semidirect |
| 140. C4×C8 | C2×D109 | semidirect |
| 195. C8 | D4×D109 | semidirect |
| 209. 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 |
| #127×D109 | 2 |
| #20295412 | 2 |
| #20295403 | 2 |
| #20295402 | 2 |
| #20295400 | 2 |
| C4×#13182012 | 2 |
| #492×C109 | 2 |
| #3151 | 109 |