Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 2. #20260814 | C2 | semidirect |
| 3. #20260488 | C2 | semidirect |
| 4. #20260464 | C2 | semidirect |
| 5. C82×C97 | C2 | semidirect |
| 41. C8×C97 | M16 | semidirect |
| 42. C8×C97 | D8 | semidirect |
| 59. C97 | #1589 | semidirect |
| 64. C82 | D97 | semidirect |
| 101. C8 | #13095494 | semidirect |
| 102. C8 | D776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D776 | 2 |
| #20260814 | 2 |
| #20260488 | 2 |
| #20260464 | 2 |
| C82×C97 | 2 |
| #1589 | 97 |