Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261366 | C2 | semidirect |
| 3. #20261045 | C2 | semidirect |
| 4. #20261034 | C2 | semidirect |
| 5. #20261024 | C2 | semidirect |
| 6. #20261019 | C2 | semidirect |
| 7. #20260775 | C2 | semidirect |
| 8. #20260761 | C2 | semidirect |
| 11. C2×#106×C97 | C2 | semidirect |
| 42. #13095511 | Q8 | semidirect |
| 124. C97 | #3084 | semidirect |
| 132. C2×#106 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261366 | 2 |
| #20261216 | 2 |
| #20261045 | 2 |
| #20261034 | 2 |
| #20261024 | 2 |
| #20261019 | 2 |
| #20260775 | 2 |
| #20260761 | 2 |
| #20260734 | 2 |
| #20260732 | 2 |
| C2×#106×C97 | 2 |
| #3084 | 97 |