Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. #20260791 | C2 | semidirect |
| 3. #20260787 | C2 | semidirect |
| 4. #20260759 | C2 | semidirect |
| 6. M16×Dic97 | C2 | semidirect |
| 7. #423×C97 | C2 | semidirect |
| 17. C4⋊#11715895 | C22 | semidirect |
| 19. #15690720 | C22 | semidirect |
| 20. C8×Dic97 | C22 | semidirect |
| 23. C4⋊C8×C97 | C22 | semidirect |
| 74. C4×D97 | M16 | semidirect |
| 97. C97 | #2920 | semidirect |
| 102. #423 | D97 | semidirect |
| 117. C4⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D97 | 2 |
| #20260791 | 2 |
| #20260787 | 2 |
| #20260759 | 2 |
| #20260698 | 2 |
| M16×Dic97 | 2 |
| #423×C97 | 2 |
| #2920 | 97 |