Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15693054 | C2 | semidirect |
| 2. C2×#15693029 | C2 | semidirect |
| 4. #20268367 | C2 | semidirect |
| 5. #20268050 | C2 | semidirect |
| 6. #20268038 | C2 | semidirect |
| 7. #20268033 | C2 | semidirect |
| 8. #20268021 | C2 | semidirect |
| 9. #20267785 | C2 | semidirect |
| 10. C2×#15692944 | C2 | semidirect |
| 11. #428×C103 | C2 | semidirect |
| 77. M16×C103 | D4 | semidirect |
| 144. C103 | #3063 | semidirect |
| 153. #428 | D103 | semidirect |
| 210. M16 | D412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15693054 | 2 |
| C2×#15693029 | 2 |
| #20268372 | 2 |
| #20268367 | 2 |
| #20268050 | 2 |
| #20268038 | 2 |
| #20268033 | 2 |
| #20268021 | 2 |
| #20267785 | 2 |
| C2×#15692944 | 2 |
| #428×C103 | 2 |
| #3063 | 103 |