Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20292777 | C2 | semidirect |
| 2. #20292760 | C2 | semidirect |
| 3. #20292536 | C2 | semidirect |
| 4. #20292364 | C2 | semidirect |
| 5. #20292361 | C2 | semidirect |
| 6. #20292351 | C2 | semidirect |
| 7. #538×C107 | C2 | semidirect |
| 41. C2×Q8×C107 | D4 | semidirect |
| 45. C2×D4×C107 | D4 | semidirect |
| 51. C4⋊C4×C107 | D4 | semidirect |
| 52. C4⋊C4×C107 | D4 | semidirect |
| 136. C107 | #1600 | semidirect |
| 137. #538 | D107 | semidirect |
| 165. C2×Q8 | C22⋊D107 | semidirect |
| 175. C2×D4 | C22⋊D107 | semidirect |
| 186. C4⋊C4 | C22⋊D107 | semidirect |
| 187. C4⋊C4 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292777 | 2 |
| #20292760 | 2 |
| #20292536 | 2 |
| #20292364 | 2 |
| #20292361 | 2 |
| #20292351 | 2 |
| #538×C107 | 2 |
| #1600 | 107 |