Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#15690818 | C2 | semidirect |
| 2. C22×#13095494 | C2 | semidirect |
| 4. #20260812 | C2 | semidirect |
| 5. #20260805 | C2 | semidirect |
| 6. #20260701 | C2 | semidirect |
| 7. #20260698 | C2 | semidirect |
| 8. #20260691 | C2 | semidirect |
| 9. #424×C97 | C2 | semidirect |
| 17. C2×#13095494 | C22 | semidirect |
| 19. C2×C8×D97 | C22 | semidirect |
| 26. #15690722 | C22 | semidirect |
| 27. #15690721 | C22 | semidirect |
| 28. C4×#11715895 | C22 | semidirect |
| 32. C4⋊C8×C97 | C22 | semidirect |
| 50. C2×#11715895 | D4 | semidirect |
| 114. C97 | #2930 | semidirect |
| 120. #424 | D97 | semidirect |
| 142. 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×#15690818 | 2 |
| C22×#13095494 | 2 |
| #20261247 | 2 |
| #20260812 | 2 |
| #20260805 | 2 |
| #20260701 | 2 |
| #20260698 | 2 |
| #20260691 | 2 |
| #424×C97 | 2 |
| #2930 | 97 |