Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×#15690817 | C2 | semidirect |
| 2. #20260736 | C2 | semidirect |
| 3. C2×#15690731 | C2 | semidirect |
| 4. C2×#15690727 | C2 | semidirect |
| 5. #20260503 | C2 | semidirect |
| 6. #20260499 | C2 | semidirect |
| 24. AGL(1,ℤ/8)×C97 | C4 | semidirect |
| 124. C97 | #1907 | semidirect |
| 135. AGL(1,ℤ/8) | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| #20260736 | 2 |
| C2×#15690731 | 2 |
| C2×#15690727 | 2 |
| #20260503 | 2 |
| #20260499 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #1907 | 97 |