Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#15690835 | C2 | semidirect |
| 2. C22×#13095496 | C2 | semidirect |
| 3. C2×#15690727 | C2 | semidirect |
| 4. C2×#15690726 | C2 | semidirect |
| 5. #20260702 | C2 | semidirect |
| 6. #20260499 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C97 | C2 | semidirect |
| 133. C97 | #2018 | semidirect |
| 135. C2×AGL(1,ℤ/8) | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C22×#13095496 | 2 |
| C2×#15690727 | 2 |
| C2×#15690726 | 2 |
| #20260702 | 2 |
| #20260499 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #2018 | 97 |