Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 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. #20261138 | C2 | semidirect |
| 5. #20260485 | C2 | semidirect |
| 6. #20260483 | C2 | semidirect |
| 7. #333×C97 | C2 | semidirect |
| 75. C97 | #1695 | semidirect |
| 82. #333 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261138 | 2 |
| #20261026 | 2 |
| #20261022 | 2 |
| #20260812 | 2 |
| #20260485 | 2 |
| #20260483 | 2 |
| #333×C97 | 2 |
| #1695 | 97 |