Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
828 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 241 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 |
|---|---|---|
| 2. C2×#15690717 | C2 | semidirect |
| 3. C22×C42×C97 | C2 | semidirect |
| 8. C2×#13095488 | C4 | semidirect |
| 43. C22×D97 | C42 | semidirect |
| 48. C2×C4×C97 | C22⋊C4 | semidirect |
| 77. C97 | #1437 | semidirect |
| 79. C22×C42 | D97 | semidirect |
| 130. C2×C4 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095488 | 2 |
| C2×#15690717 | 2 |
| C22×C42×C97 | 2 |
| #1437 | 97 |