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×#16812723 | C2 | semidirect |
| 2. #20295574 | C2 | semidirect |
| 3. #127×D109 | C2 | semidirect |
| 4. #20295414 | C2 | semidirect |
| 5. #20295402 | C2 | semidirect |
| 6. #20295399 | C2 | semidirect |
| 7. #20295398 | C2 | semidirect |
| 8. C4×#13182012 | C2 | semidirect |
| 9. #493×C109 | C2 | semidirect |
| 14. C2×#13182018 | C22 | semidirect |
| 15. C2×#13182017 | C22 | semidirect |
| 16. C2×#13182014 | C22 | semidirect |
| 18. #16812699 | C22 | semidirect |
| 22. #16812686 | C22 | semidirect |
| 26. #16812609 | C22 | semidirect |
| 27. C4×#11724784 | C22 | semidirect |
| 28. C2×D8×C109 | C22 | semidirect |
| 30. #127×C109 | C22 | semidirect |
| 31. C4×C8×C109 | C22 | semidirect |
| 48. #13182012 | D4 | semidirect |
| 85. C8×C109 | C2×D4 | semidirect |
| 86. #11724784 | C2×D4 | semidirect |
| 97. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 109. C109 | #3151 | semidirect |
| 115. #493 | D109 | semidirect |
| 126. C2×D8 | C2×D109 | semidirect |
| 133. #127 | C2×D109 | semidirect |
| 140. C4×C8 | C2×D109 | semidirect |
| 195. C8 | D4×D109 | semidirect |
| 209. C4 | #16812723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812723 | 2 |
| #20295574 | 2 |
| #127×D109 | 2 |
| #20295414 | 2 |
| #20295402 | 2 |
| #20295399 | 2 |
| #20295398 | 2 |
| C4×#13182012 | 2 |
| #493×C109 | 2 |
| #3151 | 109 |