Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812729 | C2 | semidirect |
| 3. C2×#16812687 | C2 | semidirect |
| 4. #20295248 | C2 | semidirect |
| 5. #20295241 | C2 | semidirect |
| 6. #20295050 | C2 | semidirect |
| 7. #20295034 | C2 | semidirect |
| 8. #20295030 | C2 | semidirect |
| 9. C4×#41×C109 | C2 | semidirect |
| 14. C2×#13182019 | C22 | semidirect |
| 15. C2×#13182017 | C22 | semidirect |
| 24. C4⋊#11724784 | C22 | semidirect |
| 25. #16812622 | C22 | semidirect |
| 28. C4×Q8×C109 | C22 | semidirect |
| 30. C4×D4×C109 | C22 | semidirect |
| 126. C109 | #3040 | semidirect |
| 130. C4×#41 | D109 | semidirect |
| 150. C4×Q8 | C2×D109 | semidirect |
| 152. C4×D4 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812729 | 2 |
| C2×#16812724 | 2 |
| C2×#16812687 | 2 |
| #20295248 | 2 |
| #20295241 | 2 |
| #20295050 | 2 |
| #20295034 | 2 |
| #20295030 | 2 |
| C4×#41×C109 | 2 |
| #3040 | 109 |