Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #20261815 | C2 | semidirect |
| 2. #20261781 | C2 | semidirect |
| 3. #20261779 | C2 | semidirect |
| 4. D97⋊#108 | C2 | semidirect |
| 5. #20261734 | C2 | semidirect |
| 6. #20261698 | C2 | semidirect |
| 9. #15690898 | C22 | semidirect |
| 14. #15690881 | C22 | semidirect |
| 15. #15690880 | C22 | semidirect |
| 16. #15690875 | C22 | semidirect |
| 17. #15690864 | C22 | semidirect |
| 18. C8×#87604 | C22 | semidirect |
| 20. #15690833 | C4 | semidirect |
| 21. #15690833 | C4 | semidirect |
| 24. C2×#13095498 | C4 | semidirect |
| 25. C2×D776 | C4 | semidirect |
| 27. C2×Q16×C97 | C4 | semidirect |
| 102. C97 | #2957 | semidirect |
| 115. C2×Q16 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261815 | 2 |
| #20261781 | 2 |
| #20261779 | 2 |
| D97⋊#108 | 2 |
| #20261734 | 2 |
| #20261698 | 2 |
| C2×#15690833 | 2 |
| #2957 | 97 |