Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
180 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20260812 | C2 | semidirect |
| 3. #20260462 | C2 | semidirect |
| 4. C8×#11715895 | C2 | semidirect |
| 5. #335×C97 | C2 | semidirect |
| 40. C8×C97 | M16 | semidirect |
| 43. #11715895 | D8 | semidirect |
| 59. C97 | #1589 | semidirect |
| 62. #335 | D97 | semidirect |
| 102. C8 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D776 | 2 |
| #20260812 | 2 |
| #20260462 | 2 |
| C8×#11715895 | 2 |
| #335×C97 | 2 |
| #1589 | 97 |