Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
544 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q8×Dic107 | C2 | semidirect |
| 3. #20292728 | C2 | direct (N × H) |
| 4. C2×#16812043 | C2 | semidirect |
| 5. C2×#16812033 | C2 | semidirect |
| 7. C2×#16812019 | C2 | semidirect |
| 12. Q8×Dic107 | C22 | semidirect |
| 21. #16812043 | C22 | semidirect |
| 22. #16812033 | C22 | semidirect |
| 24. #16812019 | C22 | semidirect |
| 27. C2×SD16×C107 | C4 | semidirect |
| 50. C2×Q8×C107 | C2×C4 | semidirect |
| 58. SD16×C107 | C2×C4 | semidirect |
| 59. C2×C8×C107 | C2×C4 | semidirect |
| 68. Q8×C107 | C22×C4 | semidirect |
| 87. C8×C107 | C22×C4 | semidirect |
| 106. C2×C107 | #440 | semidirect |
| 111. C107 | C2×#440 | semidirect |
| 123. C2×SD16 | Dic107 | semidirect |
| 144. C2×Q8 | C2×Dic107 | semidirect |
| 158. SD16 | C2×Dic107 | semidirect |
| 161. C2×C8 | C2×Dic107 | semidirect |
| 179. Q8 | C22×Dic107 | semidirect |
| 199. C8 | C22×Dic107 | semidirect |
| 217. C2 | #20292728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic107 | 2 |
| C2×D4×Dic107 | 2 |
| #20292728 | 2 |
| C2×#16812043 | 2 |
| C2×#16812033 | 2 |
| C2×#16812030 | 2 |
| C2×#16812019 | 2 |
| C22×SD16×C107 | 2 |
| C2×#440 | 107 |