Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20295861 | C2 | semidirect |
| 2. #20295532 | C2 | semidirect |
| 3. #20295217 | C2 | semidirect |
| 4. #20295216 | C2 | semidirect |
| 5. #20295212 | C2 | semidirect |
| 6. #20294998 | C2 | semidirect |
| 7. B(4,𝔽2)×C109 | C2 | semidirect |
| 14. C23×Dic109 | C22 | semidirect |
| 15. #16812683 | C22 | semidirect |
| 16. #16812680 | C22 | semidirect |
| 19. #16812668 | C22 | semidirect |
| 22. #16812655 | C22 | semidirect |
| 23. #16812614 | C22 | semidirect |
| 24. #16812613 | C22 | semidirect |
| 26. #120×C109 | C22 | semidirect |
| 27. #99×C109 | C22 | semidirect |
| 37. C2×Dic218 | D4 | semidirect |
| 42. C2×C22⋊D109 | D4 | semidirect |
| 49. C22×Dic109 | D4 | semidirect |
| 53. C2×C4×D109 | D4 | semidirect |
| 127. C109 | #3025 | semidirect |
| 133. B(4,𝔽2) | D109 | semidirect |
| 148. #120 | C2×D109 | semidirect |
| 154. #99 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295861 | 2 |
| #20295532 | 2 |
| #20295217 | 2 |
| #20295216 | 2 |
| #20295212 | 2 |
| #20294998 | 2 |
| B(4,𝔽2)×C109 | 2 |
| #3025 | 109 |