Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #20292757 | C2 | semidirect |
| 3. #20292754 | C2 | semidirect |
| 4. Q8×C107⋊C8 | C2 | semidirect |
| 7. C8×Q8×C107 | C2 | semidirect |
| 74. C107 | #2984 | semidirect |
| 79. C8×Q8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D107 | 2 |
| #20292757 | 2 |
| #20292754 | 2 |
| Q8×C107⋊C8 | 2 |
| #20292683 | 2 |
| #20292678 | 2 |
| C8×Q8×C107 | 2 |
| #2984 | 107 |