Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13110095 | C2 | semidirect |
| 5. #20268048 | C2 | direct (N × H) |
| 6. C2×#15692952 | C2 | semidirect |
| 7. C2×#15692946 | C2 | semidirect |
| 8. C2×#103×C103 | C2 | semidirect |
| 12. C2×#13110095 | C22 | semidirect |
| 25. #15692952 | C22 | semidirect |
| 26. #15692946 | C22 | semidirect |
| 30. #103×C103 | C22 | semidirect |
| 110. C2×C103 | #470 | semidirect |
| 116. C103 | C2×#470 | semidirect |
| 124. C2×#103 | D103 | semidirect |
| 146. #103 | C2×D103 | semidirect |
| 227. C2 | #20268048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13110095 | 2 |
| C22×#13110088 | 2 |
| C2×#15693001 | 2 |
| C2×#15692997 | 2 |
| #20268048 | 2 |
| C2×#15692952 | 2 |
| C2×#15692946 | 2 |
| C2×#103×C103 | 2 |
| C2×#470 | 103 |