Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
800 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 213 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×#16812107 | C2 | semidirect |
| 3. #20292546 | C2 | semidirect |
| 4. #20292534 | C2 | semidirect |
| 34. C22⋊Dic107 | Q8 | semidirect |
| 72. C2×Dic107 | C2×Q8 | semidirect |
| 77. C22×C107 | C4⋊Q8 | semidirect |
| 94. C107 | #2434 | semidirect |
| 171. C22 | #16812107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812107 | 2 |
| C2×#16812088 | 2 |
| #20292546 | 2 |
| #20292534 | 2 |
| #20292500 | 2 |
| C4×C22⋊Dic107 | 2 |
| C23×Q8×C107 | 2 |
| #2434 | 107 |