Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
186 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 12. #15690743 | C4 | semidirect |
| 13. #15690743 | C4 | semidirect |
| 14. #15690741 | C4 | semidirect |
| 15. #15690741 | C4 | semidirect |
| 89. C97 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260771 | 2 |
| #20260761 | 2 |
| #20260499 | 2 |
| #20260496 | 2 |
| #20260494 | 2 |
| #20260489 | 2 |
| #405×C97 | 2 |
| #1922 | 97 |