Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261407 | C2 | semidirect |
| 2. #20261101 | C2 | semidirect |
| 3. #20261083 | C2 | semidirect |
| 4. #20261032 | C2 | semidirect |
| 5. #20261022 | C2 | semidirect |
| 6. #20260930 | C2 | semidirect |
| 7. #20260930 | C2 | semidirect |
| 8. #20260866 | C2 | semidirect |
| 9. #20260845 | C2 | semidirect |
| 10. C4×#13095496 | C2 | semidirect |
| 11. #554×C97 | C2 | semidirect |
| 80. D4×C97 | #41 | semidirect |
| 130. C97 | #3366 | semidirect |
| 131. #554 | D97 | semidirect |
| 218. D4 | #13095512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261407 | 2 |
| #20261101 | 2 |
| #20261083 | 2 |
| #20261032 | 2 |
| #20261022 | 2 |
| #20260930 | 2 |
| #20260866 | 2 |
| #20260845 | 2 |
| C4×#13095496 | 2 |
| #554×C97 | 2 |
| #3366 | 97 |