Finite Group DatabasebetaFinite Group DatabasebetaOrder 13184.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20268511 | C2 | semidirect |
| 3. #20268142 | C2 | semidirect |
| 4. #20268133 | C2 | semidirect |
| 5. #20268072 | C2 | semidirect |
| 6. #20268032 | C2 | semidirect |
| 7. #20268002 | C2 | semidirect |
| 8. #20267955 | C2 | semidirect |
| 9. C4×#13110094 | C2 | semidirect |
| 10. #20267788 | C2 | semidirect |
| 11. C8×D4×C103 | C2 | semidirect |
| 126. C103 | #3302 | semidirect |
| 136. C8×D4 | D103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20268511 | 2 |
| #20268446 | 2 |
| #20268142 | 2 |
| #20268133 | 2 |
| #20268072 | 2 |
| #20268032 | 2 |
| #20268002 | 2 |
| #20267955 | 2 |
| C4×#13110094 | 2 |
| #20267788 | 2 |
| C8×D4×C103 | 2 |
| #3302 | 103 |