Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. C2×#15690743 | C2 | semidirect |
| 4. #20260633 | C2 | semidirect |
| 5. #20260497 | C2 | semidirect |
| 6. #20260490 | C2 | semidirect |
| 15. #15690731 | C4 | semidirect |
| 31. C2×#11715895 | C2×C4 | semidirect |
| 35. C4⋊Dic97 | C2×C4 | semidirect |
| 67. D4×C97 | C4⋊C4 | semidirect |
| 124. C97 | #1862 | semidirect |
| 191. D4 | #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×#15690731 | 2 |
| #20260633 | 2 |
| #20260497 | 2 |
| #20260490 | 2 |
| C2×C4×D4×C97 | 2 |
| #1862 | 97 |