Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
324 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 141 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. #15690734 | C4 | semidirect |
| 14. C4×Q8×C97 | C4 | semidirect |
| 44. Q8×C97 | C42 | semidirect |
| 82. C97 | #1763 | semidirect |
| 91. C4×Q8 | Dic97 | semidirect |
| 126. Q8 | C4×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690734 | 2 |
| C2×#15690721 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260497 | 2 |
| C2×C4×Q8×C97 | 2 |
| #1763 | 97 |