Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
620 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16812036 | C2 | semidirect |
| 2. #20292628 | C2 | semidirect |
| 3. C2×#16812026 | C2 | semidirect |
| 4. #20292530 | C2 | semidirect |
| 6. C2×#13133802 | C22 | semidirect |
| 7. C2×C4⋊Dic107 | C22 | semidirect |
| 9. C2×C4×Dic107 | C22 | semidirect |
| 16. H(5,𝔽2)×C107 | C4 | semidirect |
| 64. Q8×C107 | C22⋊C4 | semidirect |
| 71. D4×C107 | C22⋊C4 | semidirect |
| 113. C107 | #1792 | semidirect |
| 121. H(5,𝔽2) | Dic107 | semidirect |
| 177. Q8 | C22⋊Dic107 | semidirect |
| 184. D4 | C22⋊Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812036 | 2 |
| #20292628 | 2 |
| C2×#16812026 | 2 |
| #20292530 | 2 |
| C2×H(5,𝔽2)×C107 | 2 |
| #1792 | 107 |