Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. #15690746 | C4 | semidirect |
| 12. C8×Dic97 | C4 | semidirect |
| 15. #107×C97 | C4 | semidirect |
| 16. #106×C97 | C4 | semidirect |
| 65. C97 | #1772 | semidirect |
| 77. #107 | Dic97 | semidirect |
| 78. #106 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690746 | 2 |
| #20260691 | 2 |
| C2×C8×Dic97 | 2 |
| #20260494 | 2 |
| #427×C97 | 2 |
| #1772 | 97 |