Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D109⋊#131 | C2 | semidirect |
| 2. #20296095 | C2 | semidirect |
| 3. #20296018 | C2 | semidirect |
| 4. #20296017 | C2 | semidirect |
| 5. #20296016 | C2 | semidirect |
| 6. C2×#16812761 | C2 | semidirect |
| 10. D109⋊M16 | C22 | semidirect |
| 11. C2×D109⋊C8 | C22 | semidirect |
| 14. #16812778 | C22 | semidirect |
| 15. C2×C4⋊#89137 | C22 | semidirect |
| 16. #16812762 | C22 | semidirect |
| 17. #16812762 | C22 | semidirect |
| 18. #16812761 | C22 | semidirect |
| 19. #16812761 | C22 | semidirect |
| 20. #16812761 | C22 | semidirect |
| 22. #16812745 | C4 | semidirect |
| 23. #16812745 | C4 | semidirect |
| 25. #16812744 | C4 | semidirect |
| 31. H(5,𝔽2)×C109 | C4 | semidirect |
| 46. #13182030 | C2×C4 | semidirect |
| 51. #13182029 | C2×C4 | semidirect |
| 54. #13182028 | C2×C4 | semidirect |
| 59. C2×D436 | C2×C4 | semidirect |
| 68. D4×D109 | C2×C4 | semidirect |
| 75. #41×C109 | C2×C4 | semidirect |
| 77. C2×D4×C109 | C2×C4 | semidirect |
| 147. C109 | #2897 | semidirect |
| 160. H(5,𝔽2) | #89137 | semidirect |
| 193. #41 | C2×#89137 | semidirect |
| 210. C2×D4 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊#131 | 2 |
| #20296095 | 2 |
| #20296018 | 2 |
| #20296017 | 2 |
| #20296016 | 2 |
| C2×#16812761 | 2 |
| H(5,𝔽2)×D109 | 2 |
| #2897 | 109 |