Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20295826 | C2 | semidirect |
| 2. C2×#16812725 | C2 | semidirect |
| 3. C2×#16812725 | C2 | semidirect |
| 4. #20295792 | C2 | semidirect |
| 5. #20295295 | C2 | semidirect |
| 6. #20295288 | C2 | semidirect |
| 7. #20295074 | C2 | semidirect |
| 8. #20295008 | C2 | semidirect |
| 9. C2×#100×C109 | C2 | semidirect |
| 13. #16812732 | C22 | semidirect |
| 15. #16812727 | C22 | semidirect |
| 22. C2×#13182017 | C22 | semidirect |
| 24. C2×#13182014 | C22 | semidirect |
| 25. #16812707 | C22 | semidirect |
| 30. #16812634 | C22 | semidirect |
| 31. #16812617 | C22 | semidirect |
| 32. #16812615 | C22 | semidirect |
| 36. #100×C109 | C22 | semidirect |
| 148. C109 | #3068 | semidirect |
| 157. C2×#100 | D109 | semidirect |
| 184. #100 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295826 | 2 |
| C2×#16812725 | 2 |
| #20295792 | 2 |
| #20295295 | 2 |
| #20295288 | 2 |
| #20295074 | 2 |
| #20295008 | 2 |
| C2×#100×C109 | 2 |
| #3068 | 109 |