Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20261102 | C2 | semidirect |
| 4. #20261098 | C2 | semidirect |
| 5. #20261097 | C2 | semidirect |
| 6. #20261095 | C2 | semidirect |
| 7. #20261094 | C2 | semidirect |
| 8. #20260730 | C2 | semidirect |
| 9. #20260728 | C2 | semidirect |
| 10. #97×D97 | C2 | semidirect |
| 11. #489×C97 | C2 | semidirect |
| 138. C97 | #3135 | semidirect |
| 146. #489 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| #20261284 | 2 |
| #20261102 | 2 |
| #20261098 | 2 |
| #20261097 | 2 |
| #20261095 | 2 |
| #20261094 | 2 |
| #20260730 | 2 |
| #20260728 | 2 |
| #97×D97 | 2 |
| #489×C97 | 2 |
| #3135 | 97 |