Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #20296105 | C2 | semidirect |
| 2. #41×#89137 | C2 | semidirect |
| 3. #20296024 | C2 | semidirect |
| 4. #20296023 | C2 | semidirect |
| 5. D109⋊#104 | C2 | semidirect |
| 6. C2×#16812763 | C2 | semidirect |
| 10. C2×#13182039 | C22 | semidirect |
| 11. D109⋊M16 | C22 | semidirect |
| 14. #16812778 | C22 | semidirect |
| 15. C2×C4×#89137 | C22 | semidirect |
| 16. #16812764 | C22 | semidirect |
| 17. #16812764 | C22 | semidirect |
| 18. #16812763 | C22 | semidirect |
| 19. #16812763 | C22 | semidirect |
| 20. #16812763 | C22 | semidirect |
| 22. #16812746 | C4 | semidirect |
| 23. #16812746 | C4 | semidirect |
| 25. #16812744 | C4 | semidirect |
| 31. H(5,𝔽2)×C109 | C4 | semidirect |
| 49. #13182029 | C2×C4 | semidirect |
| 56. #13182028 | C2×C4 | semidirect |
| 60. C2×Dic218 | C2×C4 | semidirect |
| 62. Q8×D109 | C2×C4 | semidirect |
| 68. D4×D109 | C2×C4 | semidirect |
| 75. #41×C109 | C2×C4 | semidirect |
| 77. C2×D4×C109 | C2×C4 | semidirect |
| 140. C109 | #2901 | semidirect |
| 153. H(5,𝔽2) | #89137 | semidirect |
| 189. #41 | C2×#89137 | semidirect |
| 202. C2×D4 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296105 | 2 |
| #41×#89137 | 2 |
| #20296024 | 2 |
| #20296023 | 2 |
| D109⋊#104 | 2 |
| C2×#16812763 | 2 |
| #20295861 | 2 |
| #2901 | 109 |