Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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. #20295241 | C2 | semidirect |
| 4. #20295231 | C2 | semidirect |
| 5. #20295221 | C2 | semidirect |
| 6. #20295050 | C2 | semidirect |
| 7. #20295025 | C2 | semidirect |
| 8. C2×C4×D4×C109 | C2 | semidirect |
| 14. #16812699 | C22 | semidirect |
| 15. #16812696 | C22 | semidirect |
| 16. #16812687 | C22 | semidirect |
| 21. C4⋊#11724784 | C22 | semidirect |
| 22. C4⋊#11724784 | C22 | semidirect |
| 23. #16812622 | C22 | semidirect |
| 24. #16812619 | C22 | semidirect |
| 53. C2×D4×C109 | D4 | semidirect |
| 119. C4×C109 | AGL(1,ℤ/8) | semidirect |
| 130. C109 | #3036 | semidirect |
| 133. C2×C4×D4 | D109 | semidirect |
| 174. C2×D4 | D436 | semidirect |
| 250. 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 |
| #20295241 | 2 |
| #20295231 | 2 |
| #20295221 | 2 |
| #20295050 | 2 |
| #20295025 | 2 |
| C2×C4×D4×C109 | 2 |
| #3036 | 109 |