Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×#13133803 | C2 | semidirect |
| 2. C2×#16812084 | C2 | semidirect |
| 3. C2×#16812080 | C2 | semidirect |
| 4. C2×#16812031 | C2 | semidirect |
| 5. C2×(C2×D107)⋊C8 | C2 | semidirect |
| 6. #20292389 | C2 | semidirect |
| 7. C2×#102×C107 | C2 | semidirect |
| 39. C2×D428 | D4 | semidirect |
| 54. C2×C107⋊C8 | D4 | semidirect |
| 56. C4⋊Dic107 | D4 | semidirect |
| 65. C2×D4×C107 | D4 | semidirect |
| 72. C4⋊C4×C107 | D4 | semidirect |
| 94. C22×D107 | D8 | semidirect |
| 172. C107 | #1999 | semidirect |
| 177. C2×#102 | D107 | semidirect |
| 221. C2×D4 | D428 | semidirect |
| 242. C4⋊C4 | C22⋊D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133803 | 2 |
| C2×#16812084 | 2 |
| C2×#16812080 | 2 |
| C2×#16812031 | 2 |
| C2×(C2×D107)⋊C8 | 2 |
| #20292389 | 2 |
| C2×#102×C107 | 2 |
| #1999 | 107 |