Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
198 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 57 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×#15690753 | C2 | semidirect |
| 2. C2×#15690751 | C2 | semidirect |
| 3. #20261112 | C2 | semidirect |
| 4. #20260511 | C2 | semidirect |
| 5. #495×C97 | C2 | semidirect |
| 22. #13095486 | D4 | semidirect |
| 60. C97 | #2250 | semidirect |
| 63. #495 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| C2×#15690751 | 2 |
| #20261112 | 2 |
| #20260511 | 2 |
| #495×C97 | 2 |
| #2250 | 97 |