Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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×#16812085 | C2 | semidirect |
| 3. #20292546 | C2 | semidirect |
| 4. #20292538 | C2 | semidirect |
| 5. #20292534 | C2 | semidirect |
| 7. #20292500 | C2 | semidirect |
| 8. #20292487 | C2 | semidirect |
| 9. C23×Q8×C107 | C2 | semidirect |
| 34. C2×C22⋊D107 | Q8 | semidirect |
| 55. C2×Q8×C107 | D4 | semidirect |
| 73. C22×D107 | C2×Q8 | semidirect |
| 95. C2×Dic107 | C2×Q8 | semidirect |
| 101. C22×C107 | C22⋊Q8 | semidirect |
| 127. C107 | #2409 | semidirect |
| 128. C23×Q8 | D107 | semidirect |
| 165. C2×Q8 | C22⋊D107 | semidirect |
| 233. C22 | #16812085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812085 | 2 |
| C2×C4×C22⋊D107 | 2 |
| #20292546 | 2 |
| #20292538 | 2 |
| #20292534 | 2 |
| #20292506 | 2 |
| #20292500 | 2 |
| #20292487 | 2 |
| C23×Q8×C107 | 2 |
| #2409 | 107 |