Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20261290 | C2 | semidirect |
| 3. #20261041 | C2 | semidirect |
| 4. #20261033 | C2 | semidirect |
| 5. #20261031 | C2 | semidirect |
| 6. #20261025 | C2 | semidirect |
| 7. #20261017 | C2 | semidirect |
| 8. #20260772 | C2 | semidirect |
| 9. C4⋊C8×D97 | C2 | semidirect |
| 11. #474×C97 | C2 | semidirect |
| 44. #13095510 | Q8 | semidirect |
| 135. C97 | #3076 | semidirect |
| 143. #474 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| C4×#13095510 | 2 |
| #20261041 | 2 |
| #20261033 | 2 |
| #20261031 | 2 |
| #20261025 | 2 |
| #20261017 | 2 |
| #20260772 | 2 |
| C4⋊C8×D97 | 2 |
| #20260728 | 2 |
| #474×C97 | 2 |
| #3076 | 97 |