Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16812725 | C2 | semidirect |
| 2. #20295576 | C2 | semidirect |
| 3. #20295413 | C2 | semidirect |
| 4. #20295402 | C2 | semidirect |
| 5. #20295398 | C2 | semidirect |
| 6. C4×#13182013 | C2 | semidirect |
| 7. C2×#127×C109 | C2 | semidirect |
| 10. C2×#13182017 | C22 | semidirect |
| 11. C2×#13182014 | C22 | semidirect |
| 13. #16812699 | C22 | semidirect |
| 14. #16812696 | C22 | semidirect |
| 15. #16812687 | C22 | semidirect |
| 18. #16812610 | C22 | semidirect |
| 19. C4×#11724784 | C22 | semidirect |
| 34. #13182013 | D4 | semidirect |
| 71. #11724784 | C2×D4 | semidirect |
| 82. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 91. C109 | #3151 | semidirect |
| 94. C2×#127 | D109 | semidirect |
| 174. C4 | #16812725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812725 | 2 |
| #20295576 | 2 |
| #20295413 | 2 |
| #20295402 | 2 |
| #20295398 | 2 |
| C4×#13182013 | 2 |
| C2×#127×C109 | 2 |
| #3151 | 109 |