Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20268328 | C2 | semidirect |
| 2. #20268192 | C2 | semidirect |
| 3. #20268176 | C2 | semidirect |
| 4. #20268147 | C2 | semidirect |
| 5. #20268029 | C2 | semidirect |
| 7. #20268023 | C2 | semidirect |
| 8. C4×#13110092 | C2 | semidirect |
| 9. C4×D824 | C2 | semidirect |
| 10. C4×C8×D103 | C2 | semidirect |
| 11. C4×Q16×C103 | C2 | semidirect |
| 119. C103 | #3168 | semidirect |
| 127. C4×Q16 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268328 | 2 |
| #20268192 | 2 |
| #20268176 | 2 |
| #20268147 | 2 |
| #20268029 | 2 |
| #20268028 | 2 |
| #20268023 | 2 |
| C4×#13110092 | 2 |
| C4×D824 | 2 |
| C4×C8×D103 | 2 |
| C4×Q16×C103 | 2 |
| #3168 | 103 |