Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
298 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 15. #15690734 | C4 | semidirect |
| 58. Q8×C97 | C4⋊C4 | semidirect |
| 110. C97 | #1863 | semidirect |
| 168. Q8 | #13095490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690743 | 2 |
| C2×#15690734 | 2 |
| #20260633 | 2 |
| #20260497 | 2 |
| #20260490 | 2 |
| C2×C4×Q8×C97 | 2 |
| #1863 | 97 |