Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #20261143 | C2 | semidirect |
| 4. #20261142 | C2 | semidirect |
| 5. #20261137 | C2 | semidirect |
| 6. #20261134 | C2 | semidirect |
| 7. #20261134 | C2 | semidirect |
| 11. #499×C97 | C2 | semidirect |
| 43. #13095494 | Q8 | semidirect |
| 44. #13095494 | Q8 | semidirect |
| 100. C97 | #3166 | semidirect |
| 108. #499 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261291 | 2 |
| #125×D97 | 2 |
| #20261143 | 2 |
| #20261142 | 2 |
| #20261137 | 2 |
| #20261134 | 2 |
| #20260776 | 2 |
| #20260774 | 2 |
| C4×#13095494 | 2 |
| #499×C97 | 2 |
| #3166 | 97 |