Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20261170 | C2 | semidirect |
| 2. C2×#15690751 | C2 | semidirect |
| 3. #20261005 | C2 | semidirect |
| 4. #20260548 | C2 | semidirect |
| 5. #20260542 | C2 | semidirect |
| 6. #20260519 | C2 | semidirect |
| 7. #576×C97 | C2 | semidirect |
| 9. C2×D776 | C22 | semidirect |
| 13. #15690750 | C22 | semidirect |
| 14. C2×#13095486 | C22 | semidirect |
| 15. #15690746 | C22 | semidirect |
| 94. C97 | #2192 | semidirect |
| 95. #576 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261170 | 2 |
| C2×#15690751 | 2 |
| #20261005 | 2 |
| #20260548 | 2 |
| #20260542 | 2 |
| #20260519 | 2 |
| #576×C97 | 2 |
| #2192 | 97 |