Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
224 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 113 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. #15690745 | C4 | semidirect |
| 13. #15690743 | C4 | semidirect |
| 14. #15690741 | C4 | semidirect |
| 16. #15690720 | C4 | semidirect |
| 80. C97 | #1773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690745 | 2 |
| #20260771 | 2 |
| #20260690 | 2 |
| C2×#15690720 | 2 |
| #20260496 | 2 |
| #20260494 | 2 |
| #405×C97 | 2 |
| #1773 | 97 |