Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20260561 | C2 | semidirect |
| 4. #20260560 | C2 | semidirect |
| 5. #366×C97 | C2 | semidirect |
| 9. C16×D97 | C4 | semidirect |
| 21. #13095486 | C2×C4 | semidirect |
| 24. C16×C97 | C2×C4 | semidirect |
| 48. D97 | #366 | direct (N × H) |
| 50. C97 | C2×#366 | semidirect |
| 55. #366 | D97 | direct (N × H) |
| 74. C16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D97 | 2 |
| #107×D97 | 2 |
| #20260561 | 2 |
| #20260560 | 2 |
| #366×C97 | 2 |
| C2×#366 | 97 |