Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
332 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 157 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 | direct (N × H) |
| 14. C4×Q8×C97 | C4 | semidirect |
| 44. Q8×C97 | C42 | semidirect |
| 70. C4×C97 | #103 | semidirect |
| 81. C97 | C4×#103 | semidirect |
| 90. C4×Q8 | Dic97 | semidirect |
| 125. Q8 | C4×Dic97 | semidirect |
| 152. C4 | #15690734 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690734 | 2 |
| C2×C4×#11715895 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260497 | 2 |
| C2×C4×Q8×C97 | 2 |
| C4×#103 | 97 |