Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. M16×#87604 | C2 | semidirect |
| 4. #20261614 | C2 | semidirect |
| 13. #15690870 | C4 | semidirect |
| 18. #15690727 | C4 | semidirect |
| 19. #15690726 | C4 | semidirect |
| 20. #100×C97 | C4 | semidirect |
| 28. #13095520 | C2×C4 | semidirect |
| 40. #13095495 | C2×C4 | semidirect |
| 44. M16×C97 | C2×C4 | semidirect |
| 86. #87604 | #100 | direct (N × H) |
| 97. C97 | C4×#100 | semidirect |
| 115. #100 | #87604 | direct (N × H) |
| 135. M16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#87604 | 2 |
| D97⋊#100 | 2 |
| M16×#87604 | 2 |
| #20261614 | 2 |
| #100×D97 | 2 |
| C4×#100 | 97 |