Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#16812134 | C2 | semidirect |
| 2. C2×#16812105 | C2 | semidirect |
| 3. #20292795 | C2 | direct (N × H) |
| 4. C2×#16812036 | C2 | semidirect |
| 5. C2×#16812026 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C107 | C2 | semidirect |
| 7. C22×D428 | C22 | semidirect |
| 10. #16812134 | C22 | semidirect |
| 13. C2×#13133802 | C22 | semidirect |
| 15. #16812105 | C22 | semidirect |
| 16. C2×C4×Dic107 | C22 | semidirect |
| 17. #16812036 | C22 | semidirect |
| 18. #16812026 | C22 | semidirect |
| 21. H(5,𝔽2)×C107 | C22 | semidirect |
| 31. C2×D428 | C23 | semidirect |
| 38. #13133802 | C23 | semidirect |
| 41. C4×Dic107 | C23 | semidirect |
| 48. #41×C107 | D4 | semidirect |
| 50. C2×Q8×C107 | D4 | semidirect |
| 60. C2×D4×C107 | D4 | semidirect |
| 78. Q8×C107 | C2×D4 | semidirect |
| 85. D4×C107 | C2×D4 | semidirect |
| 123. C2×C107 | #453 | semidirect |
| 127. C107 | C2×#453 | semidirect |
| 128. C2×H(5,𝔽2) | D107 | semidirect |
| 136. H(5,𝔽2) | C2×D107 | semidirect |
| 161. #41 | C22⋊D107 | semidirect |
| 163. C2×Q8 | C22⋊D107 | semidirect |
| 179. C2×D4 | C22⋊D107 | semidirect |
| 205. Q8 | C2×C22⋊D107 | semidirect |
| 215. D4 | C2×C22⋊D107 | semidirect |
| 251. C2 | #20292795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| C2×#16812105 | 2 |
| #20292795 | 2 |
| C2×#16812036 | 2 |
| C2×#16812026 | 2 |
| C2×H(5,𝔽2)×C107 | 2 |
| C2×#453 | 107 |