Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20268589 | C2 | semidirect |
| 2. C2×#15693027 | C2 | semidirect |
| 3. #20268063 | C2 | semidirect |
| 4. #20268058 | C2 | semidirect |
| 5. #20268051 | C2 | semidirect |
| 6. C2×#15692957 | C2 | semidirect |
| 7. #20267775 | C2 | semidirect |
| 8. C2×#135×C103 | C2 | semidirect |
| 23. #15692957 | C22 | semidirect |
| 24. #15692957 | C22 | semidirect |
| 25. #15692940 | C22 | semidirect |
| 26. #15692938 | C22 | semidirect |
| 32. C2×Q16×C103 | C22 | semidirect |
| 33. C2×SD16×C103 | C22 | semidirect |
| 34. C2×D8×C103 | C22 | semidirect |
| 133. C103 | #3067 | semidirect |
| 135. C2×#135 | D103 | semidirect |
| 153. C2×Q16 | C2×D103 | semidirect |
| 154. C2×SD16 | C2×D103 | semidirect |
| 155. C2×D8 | C2×D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268589 | 2 |
| C2×#15693027 | 2 |
| #20268063 | 2 |
| #20268058 | 2 |
| #20268051 | 2 |
| C2×#15692957 | 2 |
| #20267775 | 2 |
| C2×#135×C103 | 2 |
| #3067 | 103 |