Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
156 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 4. #20260562 | C2 | semidirect |
| 5. #20260561 | C2 | semidirect |
| 6. #20260560 | C2 | semidirect |
| 7. #367×C97 | C2 | semidirect |
| 11. #15690749 | C4 | semidirect |
| 30. #13095486 | C2×C4 | semidirect |
| 34. C16×C97 | C2×C4 | semidirect |
| 64. C97 | #2159 | semidirect |
| 69. #367 | D97 | semidirect |
| 98. C16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690749 | 2 |
| #20260772 | 2 |
| #107×D97 | 2 |
| #20260562 | 2 |
| #20260561 | 2 |
| #20260560 | 2 |
| #367×C97 | 2 |
| #2159 | 97 |