Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. M16×Dic97 | C2 | semidirect |
| 5. #20260506 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 7. #430×C97 | C2 | semidirect |
| 15. #15690728 | C4 | semidirect |
| 16. #15690726 | C4 | semidirect |
| 96. C97 | #1932 | semidirect |
| 97. #430 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260751 | 2 |
| C2×#15690736 | 2 |
| #20260717 | 2 |
| M16×Dic97 | 2 |
| #20260506 | 2 |
| #20260496 | 2 |
| #430×C97 | 2 |
| #1932 | 97 |