Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#13095496 | C2 | semidirect |
| 2. C23×#11715895 | C2 | semidirect |
| 3. C2×#15690784 | C2 | semidirect |
| 4. #20260969 | C2 | direct (N × H) |
| 5. C2×#15690743 | C2 | semidirect |
| 6. C2×#15690731 | C2 | semidirect |
| 7. C2×#15690730 | C2 | semidirect |
| 8. C2×#121×C97 | C2 | semidirect |
| 12. C2×#13095496 | C22 | semidirect |
| 16. C22×#11715895 | C22 | semidirect |
| 18. #15690784 | C22 | semidirect |
| 21. #15690743 | C22 | semidirect |
| 22. #15690731 | C22 | semidirect |
| 23. #15690730 | C22 | semidirect |
| 28. #121×C97 | C22 | semidirect |
| 42. C2×#11715895 | D4 | semidirect |
| 72. C23×C97 | D8 | semidirect |
| 101. #11715895 | C2×D4 | semidirect |
| 111. C22×C97 | C2×D8 | semidirect |
| 126. C2×C97 | #466 | semidirect |
| 132. C97 | C2×#466 | semidirect |
| 136. C2×#121 | D97 | semidirect |
| 155. #121 | C2×D97 | semidirect |
| 208. C23 | #13095496 | semidirect |
| 247. C22 | C2×#13095496 | semidirect |
| 259. C2 | #20260969 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C23×#11715895 | 2 |
| C2×#15690784 | 2 |
| #20260969 | 2 |
| C2×#15690743 | 2 |
| C2×#15690731 | 2 |
| C2×#15690730 | 2 |
| C2×#121×C97 | 2 |
| C2×#466 | 97 |