Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C2×#15690831 | C2 | semidirect |
| 2. C2×#15690829 | C2 | semidirect |
| 3. #20261284 | C2 | semidirect |
| 4. #20261283 | C2 | semidirect |
| 5. #20261130 | C2 | semidirect |
| 6. #20261129 | C2 | semidirect |
| 7. #20261126 | C2 | semidirect |
| 8. #20261123 | C2 | semidirect |
| 9. #20261122 | C2 | semidirect |
| 10. #97×D97 | C2 | semidirect |
| 11. #496×C97 | C2 | semidirect |
| 64. C8×D97 | D4 | semidirect |
| 134. C97 | #3150 | semidirect |
| 144. #496 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690831 | 2 |
| C2×#15690829 | 2 |
| #20261284 | 2 |
| #20261283 | 2 |
| #20261130 | 2 |
| #20261129 | 2 |
| #20261126 | 2 |
| #20261123 | 2 |
| #20261122 | 2 |
| #97×D97 | 2 |
| #496×C97 | 2 |
| #3150 | 97 |