Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. Q8×D388 | C2 | semidirect |
| 2. #20261081 | C2 | semidirect |
| 3. #20261015 | C2 | semidirect |
| 4. #20260927 | C2 | semidirect |
| 5. Q8×#11715895 | C2 | semidirect |
| 6. C4×#13095496 | C2 | semidirect |
| 7. #550×C97 | C2 | semidirect |
| 46. Q8×C97 | D8 | semidirect |
| 58. D388 | #41 | semidirect |
| 82. C97 | #3358 | semidirect |
| 83. #550 | D97 | semidirect |
| 129. Q8 | #13095496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D388 | 2 |
| #20261081 | 2 |
| #20261015 | 2 |
| #20260927 | 2 |
| Q8×#11715895 | 2 |
| C4×#13095496 | 2 |
| #550×C97 | 2 |
| #3358 | 97 |