Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 47 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×#15690753 | C2 | semidirect |
| 2. C2×#15690749 | C2 | semidirect |
| 3. #20260973 | C2 | semidirect |
| 5. #20260560 | C2 | semidirect |
| 6. #20260537 | C2 | semidirect |
| 7. #358×C97 | C2 | semidirect |
| 33. #13095486 | D4 | semidirect |
| 76. C97 | #2220 | semidirect |
| 82. #358 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690753 | 2 |
| C2×#15690749 | 2 |
| #20260973 | 2 |
| #20260972 | 2 |
| #20260560 | 2 |
| #20260537 | 2 |
| #358×C97 | 2 |
| #2220 | 97 |