Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
616 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×C8×D97 | C2 | semidirect |
| 3. C2×#15690785 | C2 | semidirect |
| 4. C2×#15690781 | C2 | semidirect |
| 5. #20260970 | C2 | direct (N × H) |
| 6. C2×#15690743 | C2 | semidirect |
| 7. C2×#15690732 | C2 | semidirect |
| 8. C2×#102×C97 | C2 | semidirect |
| 14. C2×#13095496 | C22 | semidirect |
| 17. C2×C8×D97 | C22 | semidirect |
| 19. #15690785 | C22 | semidirect |
| 21. #15690781 | C22 | semidirect |
| 25. #15690743 | C22 | semidirect |
| 26. #15690732 | C22 | semidirect |
| 30. #102×C97 | C22 | semidirect |
| 48. C2×#11715895 | D4 | semidirect |
| 77. C22×D97 | D8 | semidirect |
| 101. #11715895 | C2×D4 | semidirect |
| 117. C2×D97 | C2×D8 | semidirect |
| 125. C2×C97 | #466 | semidirect |
| 132. C97 | C2×#466 | semidirect |
| 140. C2×#102 | D97 | semidirect |
| 162. #102 | C2×D97 | semidirect |
| 259. C2 | #20260970 | 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 |
| C22×C8×D97 | 2 |
| C2×#15690785 | 2 |
| C2×#15690781 | 2 |
| #20260970 | 2 |
| C2×#15690743 | 2 |
| C2×#15690732 | 2 |
| C2×#102×C97 | 2 |
| C2×#466 | 97 |