Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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. C8×Dic214 | C2 | semidirect |
| 3. #20292379 | C2 | semidirect |
| 4. #20292357 | C2 | semidirect |
| 6. #20292349 | C2 | semidirect |
| 53. Dic214 | M16 | semidirect |
| 78. C107 | #1588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic214 | 2 |
| C4×#13133806 | 2 |
| #20292379 | 2 |
| #20292357 | 2 |
| D4⋊(C107⋊C8) | 2 |
| #20292349 | 2 |
| #436×C107 | 2 |
| #1588 | 107 |