Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20268404 | C2 | direct (N × H) |
| 2. C2×#15693021 | C2 | semidirect |
| 4. C2×#15693012 | C2 | semidirect |
| 6. C2×#15692986 | C2 | semidirect |
| 8. C2×#125×C103 | C2 | semidirect |
| 11. #15693021 | C22 | semidirect |
| 13. #15693012 | C22 | semidirect |
| 15. #15692986 | C22 | semidirect |
| 25. #125×C103 | C22 | semidirect |
| 81. C2×C103 | #541 | semidirect |
| 86. C103 | C2×#541 | semidirect |
| 91. C2×#125 | D103 | semidirect |
| 100. #125 | C2×D103 | semidirect |
| 168. C2 | #20268404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268404 | 2 |
| C2×#15693021 | 2 |
| C2×#15693016 | 2 |
| C2×#15693012 | 2 |
| C2×#15693001 | 2 |
| C2×#15692986 | 2 |
| C2×#15692978 | 2 |
| C2×#125×C103 | 2 |
| C2×#541 | 103 |