Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 11. C4⋊Q8×C97 | C4 | semidirect |
| 12. C4⋊Q8×C97 | C4 | semidirect |
| 17. C4×Q8×C97 | C4 | semidirect |
| 79. C97 | #1518 | semidirect |
| 84. C4⋊Q8 | Dic97 | semidirect |
| 85. C4⋊Q8 | Dic97 | semidirect |
| 90. C4×Q8 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260788 | 2 |
| #20260601 | 2 |
| #20260472 | 2 |
| #533×C97 | 2 |
| #1518 | 97 |