Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20260552 | C2 | semidirect |
| 5. #20260551 | C2 | semidirect |
| 6. #20260550 | C2 | semidirect |
| 7. #362×C97 | C2 | semidirect |
| 88. D97 | #362 | direct (N × H) |
| 90. C97 | C2×#362 | semidirect |
| 97. #362 | D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| M32×D97 | 2 |
| #108×D97 | 2 |
| #20260552 | 2 |
| #20260551 | 2 |
| #20260550 | 2 |
| #362×C97 | 2 |
| C2×#362 | 97 |