Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #20260853 | C2 | semidirect |
| 3. #20260564 | C2 | semidirect |
| 4. #20260542 | C2 | semidirect |
| 5. #20260541 | C2 | semidirect |
| 6. #20260511 | C2 | semidirect |
| 7. #443×C97 | C2 | semidirect |
| 10. #15690756 | C4 | semidirect |
| 11. #15690754 | C4 | semidirect |
| 12. #15690753 | C4 | semidirect |
| 13. #15690751 | C4 | semidirect |
| 72. C97 | #2179 | semidirect |
| 75. #443 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261165 | 2 |
| #20260853 | 2 |
| #20260564 | 2 |
| #20260542 | 2 |
| #20260541 | 2 |
| #20260511 | 2 |
| #443×C97 | 2 |
| #2179 | 97 |