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. #20261306 | C2 | semidirect |
| 2. C2×#15690797 | C2 | semidirect |
| 3. C2×#15690737 | C2 | semidirect |
| 4. #20260740 | C2 | semidirect |
| 5. C2×#15690728 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 131. C97 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261306 | 2 |
| C2×#15690797 | 2 |
| C2×#15690737 | 2 |
| #20260740 | 2 |
| C2×#15690728 | 2 |
| #20260496 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #2003 | 97 |