Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #20296106 | C2 | semidirect |
| 2. #20296072 | C2 | semidirect |
| 3. #20296070 | C2 | semidirect |
| 4. D109⋊#108 | C2 | semidirect |
| 5. #20296025 | C2 | semidirect |
| 6. #20295989 | C2 | semidirect |
| 9. #16812787 | C22 | semidirect |
| 14. #16812770 | C22 | semidirect |
| 15. #16812769 | C22 | semidirect |
| 16. #16812764 | C22 | semidirect |
| 17. #16812753 | C22 | semidirect |
| 18. C8×#89137 | C22 | semidirect |
| 20. #16812722 | C4 | semidirect |
| 21. #16812722 | C4 | semidirect |
| 24. C2×#13182016 | C4 | semidirect |
| 25. C2×D872 | C4 | semidirect |
| 27. C2×Q16×C109 | C4 | semidirect |
| 102. C109 | #2957 | semidirect |
| 115. C2×Q16 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296106 | 2 |
| #20296072 | 2 |
| #20296070 | 2 |
| D109⋊#108 | 2 |
| #20296025 | 2 |
| #20295989 | 2 |
| C2×#16812722 | 2 |
| #2957 | 109 |