Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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. #20261139 | C2 | semidirect |
| 3. #20260561 | C2 | semidirect |
| 4. #20260560 | C2 | semidirect |
| 5. #20260553 | C2 | semidirect |
| 30. D8×C97 | Q8 | semidirect |
| 64. C97 | #2224 | semidirect |
| 87. D8 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261139 | 2 |
| D8×Dic97 | 2 |
| #20260561 | 2 |
| #20260560 | 2 |
| #20260553 | 2 |
| #20260536 | 2 |
| #357×C97 | 2 |
| #2224 | 97 |